Terminplan Berufungsvorträge

Berufungsverfahren: Stochastik
Montag, 25.04.2016, HS E
Dr. Denis DENISOV
School of Mathematics, University of Manchester
08.30 – 09.15
Vortrag mit Diskussion
Asymptotics for exit times of random walks and Markov chains
The classical Wiener-Hopf-factorisation has been a powerful tool for the analysis
of exit times of one-dimensional random walks for more than fifty years. The
factorisation is based on duality for random walks, which, in general, is not
available in higher dimensions or when random walk is not homogeneous in
time (or space).
I will talk about a new method that combines analytical approach via harmonic
functions and probabilistic universality approach that approximates random
walks with Brownian motion. This method allows to find the tail asymptotics for
the exit time and prove integral and local limit theorems for a multidimensional
random walk conditioned to stay in a cone. I will also discuss further extensions
of the method to Markov chains and non-homogeneous random walks.
Prof. Dr. Leif DÖRING
Institut für Mathematik, Universität Mannheim
11.30 – 12.15
Vortrag mit Diskussion
Über Singuläre Stochastische Differentialgleichungen
Prof. Dr. Erika HAUSENBLAS
Lehrstuhl für Angewandte Mathematik, Montanuniversität Leoben
Vortrag mit Diskussion
14.45 – 15.30
Nonlinear Filtering with Levy processes
In many problems arising from physics, engineering, finance and many other
applied sciences the state of a dynamical system cannot be measured directly
and has to be estimated from observations. In general, observations made on a
dynamical system are corrupted by random errors. To extract from them the
most precise information about the underlying system, it is important and
necessary to filter out the noise in the observations.
In the talk we consider the situation where both, the state process X and the
observation process Y, are described by a stochastic differential equation
perturbed by Levy processes which are not independent. More precisely,
L=(L1,L2) is a two dimensional Levy process whose structure of dependence is
described by a Levy copula. In our situation the state process (resp., the
observation) solves stochastic differential equation driven by L1 (resp., L2). We
derive the associated Zakai equation for the so called density process. We also
establish sufficient conditions depending on the copula and $L$ for the
existence and uniqueness of the corresponding solution to the Zakai equation.
Moreover, we give conditions of existence and uniqueness of the density
process, for the case where one is interested to estimate quantities like P(X(t) >
a), where a belongs to the real numbers.
Dienstag, 26.04.2016, HS E
Jun.-Prof. Dr. Matthias MEINERS
Fachbereich Mathematik, Technische Universität Darmstadt
08.30 – 09.15
Vortrag mit Diskussion
Solutions to complex smoothing equations
In several models of applied probability such as Pólya urns, search trees, and
fragmentation processes, the limiting behavior of quantities of interest is
described by distributions on the complex plane that solve smoothing
equations. Also the stationary solutions of certain 3-dimensional kinetic-type
evolution equations satisfy smoothing equations with random similarity
matrices as coefficients.
In my talk, I will consider smoothing equations in dimension d with random
similarities as coefficients. This is a unified framework which covers all
equations appearing in the examples listed above. The main focus of the talk is
on the problem of determining all solutions to these equations.
The talk is based on joint work with Sebastian Mentemeier (Dortmund).
Assistenzprofessor Dr. Sebastian MÜLLER
Aix-Marseille Université
Vortrag mit Diskussion
11.30 – 12.15
Random walk: between theory and application
The theory of random walks is a very active research area that lies in between
several branches of mathematics and has numerously many applications.
In the first part we summarize some classic results of random walk theory and
their applications. In the second part we give a brief (and non-technical)
overview over my recent research activities on random walks in random media
and random walks on groups.
Mittwoch, 27.04.2016, HS E
Prof. Dr. Stefan TAPPE
Institut für Mathematische Stochastik, Leibnitz Universität Hannover
08.30 – 09.15
Vortrag mit Diskussion
Invariance of closed convex cones for stochastic partial differential equations
The goal of this talk is to clarify when a closed convex cone is invariant for a
stochastic partial differential equation (SPDE) driven by a Wiener process and a
Poisson random measure, and to provide conditions on the parameters of the
SPDE, which are necessary and sufficient.
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