TY - THES
A1 - Kolb, Martin
T1 - On the Large Time Behavior of Diffusions: Results Between Analysis and Probability
N2 - Limit theorems constitute a classical and important field in probability theory. In several applications, in particular in demographic or medical contexts, killed Markov processes suggest themselves as models for populations undergoing culling by mortality or other processes. In these situations mathematical research features a general interest in the observable distribution of survivors, which is known as Yaglom limit or quasi-stationary distribution. Previous work often focuses on discrete state spaces, commonly birth-death processes (or with some more flexible localization of the transitions), with killing only on the boundary. The central concerns of this thesis are to describe, for a given class of one dimensional diffusion processes, the quasistationary distributions (if any), and to describe the convergence (or not) of the process conditioned on survival to one of these quasistationary distributions. Rather general diffusion processes on the half-line are considered, where 0 is allowed to be regular or an exit boundary. Very similar techniques are applied in this work in order to derive results on the large time behavior of an exotic measure valued process, which is closely related to so-called point interactions, which have been widely studied in the mathematical physics literature.
N2 - Zum Langzeit-Verhalten von Diffusionsprozessen: Resultate zwischen Analysis und Wahrscheinlichkeitstheorie
KW - Diffusion processes
KW - Yaglom limits
KW - limit theorems
Y1 - 2009
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2183
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-24821
ER -