TY - JOUR A1 - Wallenta, Daniel T1 - A Lefschetz fixed point formula for elliptic quasicomplexes JF - Integral equations and operator theor N2 - In a recent paper, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes. KW - Elliptic complexes KW - Fredholm complexes KW - Lefschetz number Y1 - 2014 U6 - https://doi.org/10.1007/s00020-014-2122-4 SN - 0378-620X SN - 1420-8989 VL - 78 IS - 4 SP - 577 EP - 587 PB - Springer CY - Basel 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 - JOUR A1 - Klein, Markus A1 - Leonard, Christian A1 - Rosenberger, Elke T1 - Agmon-type estimates for a class of jump processes JF - Mathematische Nachrichten N2 - In the limit 0 we analyse the generators H of families of reversible jump processes in Rd associated with a class of symmetric non-local Dirichlet-forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of a certain eikonal equation. Fine results are sensitive to the rate function being C2 or just Lipschitz. Our estimates are analogous to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice Zd. Although our final interest is in the (sub)stochastic jump process, technically this is a pure analysis paper, inspired by PDE techniques. KW - Decay of eigenfunctions KW - semiclassical Agmon estimate KW - Finsler distance KW - jump process KW - Dirichlet-form Y1 - 2014 U6 - https://doi.org/10.1002/mana.201200324 SN - 0025-584X SN - 1522-2616 VL - 287 IS - 17-18 SP - 2021 EP - 2039 PB - Wiley-VCH CY - Weinheim ER - TY - INPR A1 - Fedchenko, Dmitry A1 - Tarkhanov, Nikolai Nikolaevich T1 - An index formula for Toeplitz operators N2 - We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first order partial differential equations in a bounded domain of Euclidean space with infinitely differentiable boundary. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3(2014)12 KW - Toeplitz operators KW - Fredholm property KW - index Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72499 SN - 2193-6943 VL - 3 IS - 12 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Aizenberg, Lev A. A1 - Tarkhanov, Nikolai Nikolaevich T1 - An integral formula for the number of lattice points in a domain N2 - Using the multidimensional logarithmic residue we show a simple formula for the difference between the number of integer points in a bounded domain of R^n and the volume of this domain. The difference proves to be the integral of an explicit differential form over the boundary of the domain. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 3 KW - logarithmic residue KW - lattice point Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70453 SN - 2193-6943 VL - 3 IS - 3 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - BOOK A1 - Pilipenko, Andrey T1 - An introduction to stochastic differential equations with reflection T3 - Lectures in pure and applied mathematics N2 - These lecture notes are intended as a short introduction to diffusion processes on a domain with a reflecting boundary for graduate students, researchers in stochastic analysis and interested readers. Specific results on stochastic differential equations with reflecting boundaries such as existence and uniqueness, continuity and Markov properties, relation to partial differential equations and submartingale problems are given. An extensive list of references to current literature is included. This book has its origins in a mini-course the author gave at the University of Potsdam and at the Technical University of Berlin in Winter 2013. T3 - Lectures in pure and applied mathematics - 1 KW - Diffusionsprozess KW - Reflektierende Randbedingungen KW - stochastische Differentialgleichungen KW - diffusion process KW - reflecting boundary KW - stochastic differential equations Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70782 SN - 978-3-86956-297-1 SN - 2199-4951 SN - 2199-496X IS - 1 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Baerenzung, Julien A1 - Holschneider, Matthias A1 - Lesur, Vincent T1 - Bayesian inversion for the filtered flow at the Earth's core-mantle boundary JF - Journal of geophysical research : Solid earth N2 - The inverse problem of determining the flow at the Earth's core-mantle boundary according to an outer core magnetic field and secular variation model has been investigated through a Bayesian formalism. To circumvent the issue arising from the truncated nature of the available fields, we combined two modeling methods. In the first step, we applied a filter on the magnetic field to isolate its large scales by reducing the energy contained in its small scales, we then derived the dynamical equation, referred as filtered frozen flux equation, describing the spatiotemporal evolution of the filtered part of the field. In the second step, we proposed a statistical parametrization of the filtered magnetic field in order to account for both its remaining unresolved scales and its large-scale uncertainties. These two modeling techniques were then included in the Bayesian formulation of the inverse problem. To explore the complex posterior distribution of the velocity field resulting from this development, we numerically implemented an algorithm based on Markov chain Monte Carlo methods. After evaluating our approach on synthetic data and comparing it to previously introduced methods, we applied it to a magnetic field model derived from satellite data for the single epoch 2005.0. We could confirm the existence of specific features already observed in previous studies. In particular, we retrieved the planetary scale eccentric gyre characteristic of flow evaluated under the compressible quasi-geostrophy assumption although this hypothesis was not considered in our study. In addition, through the sampling of the velocity field posterior distribution, we could evaluate the reliability, at any spatial location and at any scale, of the flow we calculated. The flow uncertainties we determined are nevertheless conditioned by the choice of the prior constraints we applied to the velocity field. Y1 - 2014 U6 - https://doi.org/10.1002/2013JB010358 SN - 2169-9313 SN - 2169-9356 VL - 119 IS - 4 SP - 2695 EP - 2720 PB - American Geophysical Union CY - Washington ER - TY - INPR A1 - Conforti, Giovanni A1 - Léonard, Christian A1 - Murr, Rüdiger A1 - Roelly, Sylvie T1 - Bridges of Markov counting processes : reciprocal classes and duality formulas N2 - Processes having the same bridges are said to belong to the same reciprocal class. In this article we analyze reciprocal classes of Markov counting processes by identifying their reciprocal invariants and we characterize them as the set of counting processes satisfying some duality formula. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 9 KW - counting process KW - bridge KW - reciprocal class KW - duality formula Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-71855 SN - 2193-6943 VL - 3 IS - 9 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Holschneider, Matthias A1 - Zöller, Gert A1 - Clements, R. A1 - Schorlemmer, Danijel T1 - Can we test for the maximum possible earthquake magnitude? JF - Journal of geophysical research : Solid earth Y1 - 2014 U6 - https://doi.org/10.1002/2013JB010319 SN - 2169-9313 SN - 2169-9356 VL - 119 IS - 3 SP - 2019 EP - 2028 PB - American Geophysical Union CY - Washington ER - TY - THES A1 - Supaporn, Worakrit T1 - Categorical equivalence of clones Y1 - 2014 ER -