@unpublished{PaneahSchulze1998,
  author    = {Paneah, Boris and Schulze, Bert-Wolfgang},
  title     = {On the existence of smooth solutions of the dirichlet problem for hyperbolic : differential equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25179},
  year      = {1998},
  language  = {en}
}
@unpublished{Davis2002,
  author    = {Davis, Simon},
  title     = {On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26474},
  year      = {2002},
  abstract  = {The Goldbach partitions of an even number greater than 2, given by the sums of two prime addends, form the non-empty set for all integers 2n with 2 ≤ n ≤ 2 × 1014. It will be shown how to determine by the method of induction the existence of a non-zero lower bound for the number of Goldbach partitions of all even integers greater than or equal to 4. The proof depends on contour arguments for complex functions in the unit disk.},
  language  = {en}
}
@phdthesis{Mazzonetto2016,
  author    = {Mazzonetto, Sara},
  title     = {On the exact simulation of (skew) Brownian diffusions with discontinuous drift},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-102399},
  school      = {Universit{\"a}t Potsdam},
  pages     = {ii, 100},
  year      = {2016},
  abstract  = {This thesis is focused on the study and the exact simulation of two classes of real-valued Brownian diffusions: multi-skew Brownian motions with constant drift and Brownian diffusions whose drift admits a finite number of jumps. The skew Brownian motion was introduced in the sixties by It{\^o} and McKean, who constructed it from the reflected Brownian motion, flipping its excursions from the origin with a given probability. Such a process behaves as the original one except at the point 0, which plays the role of a semipermeable barrier. More generally, a skew diffusion with several semipermeable barriers, called multi-skew diffusion, is a diffusion everywhere except when it reaches one of the barriers, where it is partially reflected with a probability depending on that particular barrier. Clearly, a multi-skew diffusion can be characterized either as solution of a stochastic differential equation involving weighted local times (these terms providing the semi-permeability) or by its infinitesimal generator as Markov process. In this thesis we first obtain a contour integral representation for the transition semigroup of the multiskew Brownian motion with constant drift, based on a fine analysis of its complex properties. Thanks to this representation we write explicitly the transition densities of the two-skew Brownian motion with constant drift as an infinite series involving, in particular, Gaussian functions and their tails. Then we propose a new useful application of a generalization of the known rejection sampling method. Recall that this basic algorithm allows to sample from a density as soon as one finds an - easy to sample - instrumental density verifying that the ratio between the goal and the instrumental densities is a bounded function. The generalized rejection sampling method allows to sample exactly from densities for which indeed only an approximation is known. The originality of the algorithm lies in the fact that one finally samples directly from the law without any approximation, except the machine's. As an application, we sample from the transition density of the two-skew Brownian motion with or without constant drift. The instrumental density is the transition density of the Brownian motion with constant drift, and we provide an useful uniform bound for the ratio of the densities. We also present numerical simulations to study the efficiency of the algorithm. The second aim of this thesis is to develop an exact simulation algorithm for a Brownian diffusion whose drift admits several jumps. In the literature, so far only the case of a continuous drift (resp. of a drift with one finite jump) was treated. The theoretical method we give allows to deal with any finite number of discontinuities. Then we focus on the case of two jumps, using the transition densities of the two-skew Brownian motion obtained before. Various examples are presented and the efficiency of our approach is discussed.},
  language  = {en}
}
@unpublished{GibaliShoikhetTarkhanov2015,
  author    = {Gibali, Aviv and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich},
  title     = {On the convergence of continuous Newton method},
  volume    = {4},
  number    = {10},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-81537},
  pages     = {15},
  year      = {2015},
  abstract  = {In this paper we study the convergence of continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on a recent progress in the geometric theory of spirallike functions. We prove convergence theorems and illustrate them by numerical simulations.},
  language  = {en}
}
@unpublished{NehringPoghosyanZessin2013,
  author    = {Nehring, Benjamin and Poghosyan, Suren and Zessin, Hans},
  title     = {On the construction of point processes in statistical mechanics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64080},
  year      = {2013},
  abstract  = {By means of the cluster expansion method we show that a recent result of Poghosyan and Ueltschi (2009) combined with a result of Nehring (2012) yields a construction of point processes of classical statistical mechanics as well as processes related to the Ginibre Bose gas of Brownian loops and to the dissolution in R^d of Ginibre's Fermi-Dirac gas of such loops. The latter will be identified as a Gibbs perturbation of the ideal Fermi gas. On generalizing these considerations we will obtain the existence of a large class of Gibbs perturbations of the so-called KMM-processes as they were introduced by Nehring (2012). Moreover, it is shown that certain "limiting Gibbs processes" are Gibbs in the sense of Dobrushin, Lanford and Ruelle if the underlying potential is positive. And finally, Gibbs modifications of infinitely divisible point processes are shown to solve a new integration by parts formula if the underlying potential is positive.},
  language  = {en}
}
@unpublished{EgorovKondratievSchulze2004,
  author    = {Egorov, Jurij V. and Kondratiev, V. A. and Schulze, Bert-Wolfgang},
  title     = {On the completeness of root functions of elliptic boundary problems in a domain with conical points on the boundary},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26773},
  year      = {2004},
  abstract  = {Contents: 1 Introduction 2 Definitions 3 Rays of minimal growth 4 Proof of Theorem 2. 5 The growth of the resolvent 6 Proof of Theorem 3. 7 The completeness of root functions 8 Some generalizations},
  language  = {en}
}
@unpublished{GairingHoegeleKosenkovaetal.2014,
  author    = {Gairing, Jan and H{\"o}gele, Michael and Kosenkova, Tetiana and Kulik, Alexei Michajlovič},
  title     = {On the calibration of L{\´e}vy driven time series with coupling distances : an application in paleoclimate},
  volume    = {3},
  number    = {2},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-69781},
  pages     = {18},
  year      = {2014},
  abstract  = {This article aims at the statistical assessment of time series with large fluctuations in short time, which are assumed to stem from a continuous process perturbed by a L{\´e}vy process exhibiting a heavy tail behavior. We propose an easily implementable procedure to estimate efficiently the statistical difference between the noisy behavior of the data and a given reference jump measure in terms of so-called coupling distances. After a short introduction to L{\´e}vy processes and coupling distances we recall basic statistical approximation results and derive rates of convergence. In the sequel the procedure is elaborated in detail in an abstract setting and eventually applied in a case study to simulated and paleoclimate data. It indicates the dominant presence of a non-stable heavy-tailed jump L{\´e}vy component for some tail index greater than 2.},
  language  = {en}
}
@unpublished{Krainer2002,
  author    = {Krainer, Thomas},
  title     = {On the calculus of pseudodifferential operators with an anisotropic analytic parameter},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26200},
  year      = {2002},
  abstract  = {We introduce the Volterra calculus of pseudodifferential operators with an anisotropic analytic parameter based on "twisted" operator-valued Volterra symbols. We establish the properties of the symbolic and operational calculi, and we give and make use of explicit oscillatory integral formulas on the symbolic side. In particular, we investigate the kernel cut-off operator via direct oscillatory integral techniques purely on symbolic level. We discuss the notion of parabolic for the calculus of Volterra operators, and construct Volterra parametrices for parabolic operators within the calculus.},
  language  = {en}
}
@unpublished{Myslivets2000,
  author    = {Myslivets, Simona},
  title     = {On the boundary behaviour of the logarithmic residue integral},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25733},
  year      = {2000},
  abstract  = {A formula of multidimensional logarithmic residue is proved for holomorphic maps with zeroes on the boundary of a bounded domain in Cn.},
  language  = {en}
}
@unpublished{Davis2002,
  author    = {Davis, Simon},
  title     = {On the absence of large-order divergences in superstring theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26452},
  year      = {2002},
  abstract  = {The genus-dependence of multi-loop superstring ams is estimated at large orders in perturbation theory using the super-Schottky group parameterization of supermoduli space. Restriction of the integration region to a subset of supermoduli space and a single fundamental domain of the super-modular group suggests an exponential dependence on the genus. Upper bounds for these estimates are obtained for arbitrary N-point superstring scattering amplitudes and are shown to be consistent with exact results obtained for special type II string amplitudes for orbifold or Calabi-Yau compactifications. The genus-dependence is then obtained by considering the effect of the remaining contribution to the superstring amplitudes after the coefficients of the formally divergent parts of the integrals vanish as a result of a sum over spin structures. The introduction of supersymmetry therefore leads to the elimination of large-order divergences in string pertubation theory, a result which is based only on the supersymmetric generalization of the polyakov measure and not the gauge group of the string model.},
  language  = {en}
}