Analysis of singular stochastic systems: two classes of examples / Matthias Liesenfeld ; angefertigt unter Betreuung durch Herrn Prof. Dr. Martin Kolb. Paderborn, 2021
Content
- 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