TY - INPR A1 - Pénisson, Sophie T1 - Conditional Limit Theorems for Multitype Branching Processes and Illustration in Epidemiological Risk Analysis N2 - This thesis is concerned with the issue of extinction of populations composed of different types of individuals, and their behavior before extinction and in case of a very late extinction. We approach this question firstly from a strictly probabilistic viewpoint, and secondly from the standpoint of risk analysis related to the extinction of a particular model of population dynamics. In this context we propose several statistical tools. The population size is modeled by a branching process, which is either a continuous-time multitype Bienaymé-Galton-Watson process (BGWc), or its continuous-state counterpart, the multitype Feller diffsion process. We are interested in different kinds of conditioning on nonextinction, and in the associated equilibrium states. These ways of conditioning have been widely studied in the monotype case. However the literature on multitype processes is much less extensive, and there is no systematic work establishing connections between the results for BGWc processes and those for Feller diffusion processes. In the first part of this thesis, we investigate the behavior of the population before its extinction by conditioning the associated branching process Xt on non-extinction (Xt 6= 0), or more generally on non-extinction in a near future 0 < 1 (Xt+ 0 = 0), and by letting t tend to infinity. We prove the result, new in the multitype framework and for 0 > 0, that this limit exists and is nondegenerate. This re ects a stationary behavior for the dynamics of the population conditioned on non-extinction, and provides a generalization of the so-called Yaglom limit, corresponding to the case 0 = 0. In a second step we study the behavior of the population in case of a very late extinction, obtained as the limit when 0 tends to infinity of the process conditioned by Xt+ 0 = 0. The resulting conditioned process is a known object in the monotype case (sometimes referred to as Q-process), and has also been studied when Xt is a multitype Feller diffusion process. We investigate the not yet considered case where Xt is a multitype BGWc process and prove the existence of the associated Q-process. In addition, we examine its properties, including the asymptotic ones, and propose several interpretations of the process. Finally, we are interested in interchanging the limits in t and 0, as well as in the not yet studied commutativity of these limits with respect to the high-density-type relationship between BGWc processes and Feller processes. We prove an original and exhaustive list of all possible exchanges of limit (long-time limit in t, increasing delay of extinction 0, diffusion limit). The second part of this work is devoted to the risk analysis related both to the extinction of a population and to its very late extinction. We consider a branching population model (arising notably in the epidemiological context) for which a parameter related to the first moments of the offspring distribution is unknown. We build several estimators adapted to different stages of evolution of the population (phase growth, decay phase, and decay phase when extinction is expected very late), and prove moreover their asymptotic properties (consistency, normality). In particular, we build a least squares estimator adapted to the Q-process, allowing a prediction of the population development in the case of a very late extinction. This would correspond to the best or to the worst-case scenario, depending on whether the population is threatened or invasive. These tools enable us to study the extinction phase of the Bovine Spongiform Encephalopathy epidemic in Great Britain, for which we estimate the infection parameter corresponding to a possible source of horizontal infection persisting after the removal in 1988 of the major route of infection (meat and bone meal). This allows us to predict the evolution of the spread of the disease, including the year of extinction, the number of future cases and the number of infected animals. In particular, we produce a very fine analysis of the evolution of the epidemic in the unlikely event of a very late extinction. N2 - Diese Arbeit befasst sich mit der Frage des Aussterbens von Populationen verschiedener Typen von Individuen. Uns interessiert das Verhalten vor dem Aussterben sowie insbesondere im Falle eines sehr späten Aussterbens. Wir untersuchen diese Fragestellung zum einen von einer rein wahrscheinlichkeitstheoretischen Sicht und zum anderen vom Standpunkt der Risikoanalyse aus, welche im Zusammenhang mit dem Aussterben eines bestimmten Modells der Populationsdynamik steht. In diesem Kontext schlagen wir mehrere statistische Werkzeuge vor. Die Populationsgröße wird entweder durch einen zeitkontinuierlichen mehrtyp-Bienaymé-Galton- Watson Verzweigungsprozess (BGWc) oder durch sein Analogon mit kontinuierlichem Zustandsraum, den Feller Diffusionsprozess, modelliert. Wir interessieren uns für die unterschiedlichen Arten auf Überleben zu bedingen sowie für die hierbei auftretenden Gleichgewichtszustände. Diese Bedingungen wurden bereits weitreichend im Falle eines einzelnen Typen studiert. Im Kontext von mehrtyp-Verzweigungsprozessen hingegen ist die Literatur weniger umfangreich und es gibt keine systematischen Arbeiten, welche die Ergebnisse von BGWc Prozessen mit denen der Feller Diffusionsprozesse verbinden. Wir versuchen hiermit diese Lücke zu schliessen. Im ersten Teil dieser Arbeit untersuchen wir das Verhalten von Populationen vor ihrem Aussterben, indem wir das zeitasymptotysche Verhalten des auf Überleben bedingten zugehörigen Verzweigungsprozesses (Xt / Xt 6= 0)t betrachten (oder allgemeiner auf Überleben in naher Zukunft 0 < 1, (Xt / Xt+ 0 = 0)t). Wir beweisen das Ergebnis, neuartig im mehrtypen Rahmen und für 0 > 0, dass dieser Grenzwert existiert und nicht-degeneriert ist. Dies spiegelt ein stationäres Verhalten für auf Überleben bedingte Bevölkerungsdynamiken wider und liefert eine Verallgemeinerung des sogenannten Yaglom Grenzwertes (welcher dem Fall 0 = 0 entspricht). In einem zweiten Schritt studieren wir das Verhalten der Populationen im Falle eines sehr späten Aussterbens, welches wir durch den Grenzübergang auf 0 > unendlich erhalten. Der resultierende Grenzwertprozess ist ein bekanntes Objekt im eintypen Fall (oftmals als Q-Prozess bezeichnet) und wurde ebenfalls im Fall von mehrtyp-Feller-Diffusionsprozessen studiert. Wir untersuchen den bisher nicht betrachteten Fall, in dem Xt ein mehrtyp-BGWc Prozess ist und beweisen die Existenz des zugeh� origen Q-Prozesses. Darüber hinaus untersuchen wir seine Eigenschaften einschließlich der asymptotischen und weisen auf mehrere Auslegungen hin. Schließlich interessieren wir uns für die Austauschbarkeit der Grenzwerte in t und 0, und die Vertauschbarkeit dieser Grenzwerte in Bezug auf die Beziehung zwischen BGWc und Feller Prozessen. Wir beweisen die Durchführbarkeit aller möglichen Grenzwertvertauschungen (Langzeitverhalten, wachsende Aussterbeverzögerung, Diffusionslimit). Der zweite Teil dieser Arbeit ist der Risikoanalyse in Bezug auf das Aussterben und das sehr späte Aussterben von Populationen gewidmet. Wir untersuchen ein Modell einer verzweigten Bevölkerung (welches vor allem im epidemiologischen Rahmen erscheint), für welche ein Parameter der Reproduktionsverteilung unbekannt ist. Wir konstruieren Sch� atzer, die an die jeweiligen Stufen der Evolution adaptiert sind (Wachstumsphase, Verfallphase sowie die Verfallphase, wenn das Aussterben sehr sp� at erwartet wird), und beweisen zudem deren asymptotische Eigenschaften (Konsistenz, Normalverteiltheit). Im Besonderen bauen wir einen für Q-Prozesse adaptierten kleinste-Quadrate-Schätzer, der eine Vorhersage der Bevölkerungsentwicklung im Fall eines sehr späten Aussterbens erlaubt. Dies entspricht dem Best- oder Worst-Case-Szenario, abhängig davon, ob die Bevölkerung bedroht oder invasiv ist. Diese Instrumente erm� oglichen uns die Betrachtung der Aussterbensphase der Bovinen spongiformen Enzephalopathie Epidemie in Großbritannien. Wir schätzen den Infektionsparameter in Bezug auf m� ogliche bestehende Quellen der horizontalen Infektion nach der Beseitigung des primären Infektionsweges (Tiermehl) im Jahr 1988. Dies ermöglicht uns eine Vorhersage des Verlaufes der Krankheit inklusive des Jahres des Aussterbens, der Anzahl von zukünftigen Fällen sowie der Anzahl infizierter Tiere. Insbesondere ermöglicht es uns die Erstellung einer sehr detaillierten Analyse des Epidemieverlaufs im unwahrscheinlichen Fall eines sehr späten Aussterbens. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 11 Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49589 ER - TY - INPR A1 - Kuxhaus, Olga T1 - Parametrische Schätzungen von elliptischen Copulafunktionen N2 - Aus dem Inhalt: Inhaltsverzeichnis Abbildungsverzeichnis Tabellenverzeichnis 1 Einleitung und Motivation 2 Multivariate Copulafunktionen 2.1 Einleitung 2.2 Satz von Sklar 2.3 Eigenschaften von Copulafunktionen 3 Abhängigkeitskonzepte 3.1 Lineare Korrelation 3.2 Copulabasierte Abhängigkeitsmaße 3.2.1 Konkordanz 3.2.2 Kendall’s und Spearman’s 3.2.3 Asymptotische Randabhängigkeit 4 Elliptische Copulaklasse 4.1 Sphärische und elliptische Verteilungen 4.2 Normal-Copula 4.3 t-Copula 5 Parametrische Schätzverfahren 5.1 Maximum-Likelihood-Methode 5.1.1 ExakteMaximum-Likelihood-Methode 5.1.2 2-stufige parametrische Maximum-Likelihood-Methode 5.1.3 2-stufige semiparametrische Maximum-Likelihood-Methode 5.2 Momentenmethode 5.3 Kendall’s -Momentenmethode 6 Parameterschätzungen für Normal- und t-Copula 6.1 Normal-Copula 6.1.1 Maximum-Likelihood-Methode 6.1.2 Momentenmethode 6.1.3 Kendall’s Momentenmethode 6.1.4 Spearman’s Momentenmethode 6.2 t-Copula 6.2.1 Verfahren 1 (exakte ML-Methode) 6.2.2 Verfahren 2 (2-stufige rekursive ML-Methode) 6.2.3 Verfahren 3 (2-stufige KM-ML-Methode) 6.2.4 Verfahren 4 (3-stufige M-ML-Methode) 7 Simulationen 7.1 Grundlagen 7.2 Parametrischer Fall 7.3 Nichtparametrischer Fall 7.4 Fazit A Programmausschnitt Literaturverzeichnis T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 09 Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51681 ER - TY - INPR A1 - Voss, Carola Regine T1 - Harness-Prozesse N2 - Harness-Prozesse finden in der Forschung immer mehr Anwendung. Vor allem gewinnen Harness-Prozesse in stetiger Zeit an Bedeutung. Grundlegende Literatur zu diesem Thema ist allerdings wenig vorhanden. In der vorliegenden Arbeit wird die vorhandene Grundlagenliteratur zu Harness-Prozessen in diskreter und stetiger Zeit aufgearbeitet und Beweise ausgeführt, die bisher nur skizziert waren. Ziel dessen ist die Existenz einer Zerlegung von Harness-Prozessen über Z beziehungsweise R+ nachzuweisen. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 13 Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49651 ER - TY - INPR A1 - Méléard, Sylvie A1 - Roelly, Sylvie T1 - A host-parasite multilevel interacting process and continuous approximations N2 - We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in these individuals. The ecological parameters of the individual dynamics depend on the number of cells of each type contained by the individual and the cell dynamics depends on the trait of the invaded individual. Our models are rooted in the microscopic description of a random (discrete) population of individuals characterized by one or several adaptive traits and cells characterized by their type. The population is modeled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation and death for individuals and birth and death for cells. The interaction between individuals (resp. between cells) is described by a competition between individual traits (resp. between cell types). We look for tractable large population approximations. By combining various scalings on population size, birth and death rates and mutation step, the single microscopic model is shown to lead to contrasting nonlinear macroscopic limits of different nature: deterministic approximations, in the form of ordinary, integro- or partial differential equations, or probabilistic ones, like stochastic partial differential equations or superprocesses. The study of the long time behavior of these processes seems very hard and we only develop some simple cases enlightening the difficulties involved. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2011, 01 KW - two-level interacting processes KW - birth-death-mutation-competition point process KW - host-parasite stochastic particle system Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51694 ER - TY - INPR A1 - Nehring, Benjamin A1 - Zessin, Hans T1 - A path integral representation of the moment measures of the general ideal Bose gas N2 - We reconsider the fundamental work of Fichtner ([2]) and exhibit the permanental structure of the ideal Bose gas again, using another approach which combines a characterization of infinitely divisible random measures (due to Kerstan,Kummer and Matthes [5, 6] and Mecke [8, 9]) with a decomposition of the moment measures into its factorial measures due to Krickeberg [4]. To be more precise, we exhibit the moment measures of all orders of the general ideal Bose gas in terms of certain path integrals. This representation can be considered as a point process analogue of the old idea of Symanzik [11] that local times and self-crossings of the Brownian motion can be used as a tool in quantum field theory. Behind the notion of a general ideal Bose gas there is a class of infinitely divisible point processes of all orders with a Levy-measure belonging to some large class of measures containing the one of the classical ideal Bose gas considered by Fichtner. It is well known that the calculation of moments of higher order of point processes are notoriously complicated. See for instance Krickeberg's calculations for the Poisson or the Cox process in [4]. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 10 Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49635 ER - TY - INPR A1 - Léonard, Christian A1 - Roelly, Sylvie A1 - Zambrini, Jean-Claude T1 - Temporal symmetry of some classes of stochastic processes N2 - In this article we analyse the structure of Markov processes and reciprocal processes to underline their time symmetrical properties, and to compare them. Our originality consists in adopting a unifying approach of reciprocal processes, independently of special frameworks in which the theory was developped till now (diffusions, or pure jump processes). This leads to some new results, too. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 7 KW - Markov processes KW - reciprocal processes KW - time symmetry Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-64599 SN - 2193-6943 ER - TY - INPR A1 - Flandoli, Franco A1 - Högele, Michael T1 - A solution selection problem with small stable perturbations N2 - The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is a general alpha-stable process. It is proved that extremal solutions are selected and the probability of selection is computed. Detailed analysis of the characteristic function of an exit time form on the half-line is performed, with a suitable decomposition in small and large jumps adapted to the singular drift. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 8 KW - stochastic differential equations KW - singular drifts KW - zero-noise limit KW - Peano phenomena KW - non-uniqueness Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-71205 SN - 2193-6943 VL - 3 IS - 8 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Makhmudov, O. I. A1 - Niyozov, I. E. T1 - Regularization of the Cauchy Problem for the System of Elasticity Theory in R up (m) N2 - In this paper we consider the regularization of the Cauchy problem for a system of second order differential equations with constant coefficients. T3 - Preprint - (2005) 22 KW - the Cauchy problem KW - Lame system KW - elliptic system KW - ill-posed problem KW - Carleman matrix KW - regularization KW - Laplace equation Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29983 ER - TY - INPR A1 - Blanchard, Gilles A1 - Mathé, Peter T1 - Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration N2 - The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which takes into account both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration this modification is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 7 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57117 ER - TY - INPR A1 - Fang, Daoyuan A1 - Xu, Jiang T1 - Asymptotic behavior of solutions to multidimensional nonisentropic hydrodynamic model for semiconductors N2 - In this paper, a global existence result of smooth solutions to the multidimen- sional nonisentropic hydrodynamic model for semiconductors is proved, under the assumption that the initial data is a perturbation of the stationary solutions for the thermal equilibrium state. The resulting evolutionary solutions converge to the stationary solutions in time asymptotically exponentially fast. T3 - Preprint - (2005) 02 KW - Multidimensional nonisentropic hydrodynamic model KW - semiconductors KW - asymptotic behavior KW - global solutions Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29767 ER - TY - INPR A1 - Galstian, Anahit A1 - Yagdjian, Karen T1 - Exponential function of pseudo-differential operators N2 - The paper is devoted to the construction of the exponential function of a matrix pseudo-differential operator which do not satisfy any of the known theorems (see, Sec.8 Ch.VIII and Sec.2 Ch.XI of [17]). The applications to the construction of the fundamental solution for the Cauchy problem for the hyperbolic operators with the characteristics of variable multiplicity are given, too. T3 - Preprint - (1997) 13 KW - pseudodifferential operators KW - exponential function KW - Gevrey classes KW - hyperbolic operators KW - multiple characteristics Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24982 ER - TY - INPR A1 - Levendorskii, Sergei Z. A1 - Boyarchenko, Svetlana I. T1 - On rational pricing of derivative securities for a familiy of non-Gaussian processes N2 - Linear and non-linear analogues of the Black-Scholes equation are derived when shocks can be described by a truncated Lévy process. A linear equation is derived under the perfect correlation assumption on returns for a derivative security and a stock, and its solutions for European put and call options are obtained. It is also shown that the solution violates the perfect correlation assumption unless a process is gaussian. Thus, for a family of truncated Lévy distributions, the perfect hedging is impossible even in the continuous time limit. A second linear analogue of the Black-Scholes equation is obtained by constructing a portfolio which eliminates fluctuations of the first order and assuming that the portfolio is risk-free; it is shown that this assumption fails unless a process is gaussian. It is shown that the di erence between solutions to the linear analogues of the Black-Scholes equations and solutions to the Black-Scholes equations are sizable. The equations and solutions can be written in a discretized approximate form which uses an observed probability distribution only. Non-linear analogues for the Black-Scholes equation are derived from the non-arbitrage condition, and approximate formulas for solutions of these equations are suggested. Assuming that a linear generalization of the Black-Scholes equation holds, we derive an explicit pricing formula for the perpetual American put option and produce numerical results which show that the difference between our result and the classical Merton's formula obtained for gaussian processes can be substantial. Our formula uses an observed distribution density, under very weak assumptions on the latter. T3 - Preprint - (1998) 07 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25196 ER - TY - INPR A1 - Levendorskii, Sergei Z. A1 - Boyarchenko, Svetlana I. T1 - Investment under uncertainty when shocks are non-gaussian T3 - Preprint - (1998) 08 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25201 ER - TY - INPR A1 - Fedosov, Boris T1 - Non-Abelian reduction in deformation quantization N2 - We consider a G-invariant star-product algebra A on a symplectic manifold (M,ω) obtained by a canonical construction of deformation quantization. Under assumptions of the classical Marsden-Weinstein theorem we define a reduction of the algebra A with respect to the G-action. The reduced algebra turns out to be isomorphic to a canonical star-product algebra on the reduced phase space B. In other words, we show that the reduction commutes with the canonical G-invariant deformation quantization. A similar statement in the framework of geometric quantization is known as the Guillemin-Sternberg conjecture (by now completely proved). T3 - Preprint - (1997) 26 KW - deformation quantization KW - Hamiltonian group action KW - moment map KW - classical and quantum reduction Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25101 ER - TY - INPR A1 - Hieber, Matthias A1 - Schrohe, Elmar T1 - Lρ spectral independence of elliptic operators via commutator estimates N2 - Let {Tsub(p) : q1 ≤ p ≤ q2} be a family of consistent Csub(0) semigroups on Lφ(Ω) with q1, q2 ∈ [1, ∞)and Ω ⊆ IRn open. We show that certain commutator conditions on Tφ and on the resolvent of its generator Aφ ensure the φ independence of the spectrum of Aφ for φ ∈ [q1, q2]. Applications include the case of Petrovskij correct systems with Hölder continuous coeffcients, Schrödinger operators, and certain elliptic operators in divergence form with real, but not necessarily symmetric, or complex coeffcients. T3 - Preprint - (1997) 17 KW - Lφ spectrum KW - spectral independence KW - elliptic systems Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25047 ER - TY - INPR A1 - Schrohe, Elmar T1 - Noncommutative residues, Dixmier's Trace, and heat trace expansions on manifolds with boundary N2 - For manifolds with boundary, we define an extension of Wodzicki's noncommutative residue to boundary value problems in Boutet de Monvel's calculus. We show that this residue can be recovered with the help of heat kernel expansions and explore its relation to Dixmier's trace. T3 - Preprint - (1999) 13 Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25486 ER - TY - INPR A1 - Nazaikinskii, Vladimir E. A1 - Sternin, Boris T1 - Surgery and the relative index in elliptic theory N2 - We prove a general theorem on the local property of the relative index for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions) this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities as well as for elliptic boundary value problems with a symmetry condition for the conormal symbol. T3 - Preprint - (1999) 17 KW - elliptic operators KW - index theory KW - surgery KW - relative index KW - manifold with singularities KW - boundary value problems Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25538 ER - TY - INPR A1 - Savin, Anton A1 - Sternin, Boris T1 - Elliptic operators in even subspaces N2 - An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established. T3 - Preprint - (1999) 10 KW - index of elliptic operators in subspaces KW - K-theory KW - eta invariant KW - Atiyah-Patodi-Singer theory KW - boundary value problems Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25461 ER - TY - INPR A1 - Fedosov, Boris T1 - Moduli spaces and deformation quantization in infinite dimensions N2 - We construct a deformation quantization on an infinite-dimensional symplectic space of regular connections on an SU(2)-bundle over a Riemannian surface of genus g ≥ 2. The construction is based on the normal form thoerem representing the space of connections as a fibration over a finite-dimensional moduli space of flat connections whose fibre is a cotangent bundle of the infinite-dimensional gauge group. We study the reduction with respect to the gauge groupe both for classical and quantum cases and show that our quantization commutes with reduction. T3 - Preprint - (1998) 27 KW - moduli space of flat connections KW - gauge group KW - star-product KW - Weyl algebras bundle KW - symplectic reduction Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25396 ER - TY - INPR A1 - Witt, Ingo T1 - On the factorization of meromorphic Mellin symbols N2 - It is prooved that mermorphic, parameter-dependet elliptic Mellin symbols can be factorized in a particular way. The proof depends on the availability of logarithms of pseudodifferential operators. As a byproduct, we obtain a characterization of the group generated by pseudodifferential operators admitting a logarithm. The factorization has applications to the theory os pseudodifferential operators on spaces with conical singularities, e.g., to the index theory and the construction of various sub-calculi of the cone calculus. T3 - Preprint - (1999) 05 Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25427 ER -