Analysis of singular stochastic systems: two classes of examples / Matthias Liesenfeld ; angefertigt unter Betreuung durch Herrn Prof. Dr. Martin Kolb. Paderborn, 2021
Inhalt
Abstract
Introduction
One-dimensional time-homogeneous SDEs
Notions of solution and uniqueness
Scale function
Speed measure and Green function
Feller's Test for Explosions
Approach using Sturm-Liouville theory
h-transformation in the sense of Doob
Stochastic Spikes
Notation
Discussion of the parameter lambda
An embedded approximate Poisson process
Applications
Conclusion
Fleming-Viot particle Systems
Notation and basic properties
Transition densities
Markov chains in general state space
(Non-)extinction criterion
Markov chain analysis
Integrability of the ergodic elements
Application of Birkhoff's ergodic theorem
Computation of the integrand ln R in Theorem 5.71
Three particles
Open problems
Properties of Hypergeometric Functions
Proof omitted in Remark 5.34
Source Codes