Global ETD Search

11	Pathwise anticipating random periodic solutions of SDEs and SPDEs with linear multiplicative noise Wu, Yue January 2014 (has links) In this thesis, we study the existence of pathwise random periodic solutions to both the semilinear stochastic differential equations with linear multiplicative noise and the semilinear stochastic partial differential equations with linear multiplicative noise in a Hilbert space. We identify them as the solutions of coupled forward-backward infinite horizon stochastic integral equations in general cases, and then perform the argument of the relative compactness of Wiener-Sobolev spaces in C([0, T],L2Ω,Rd)) or C([0, T],L2(Ω x O)) and Schauder's fixed point theorem to show the existence of a solution of the coupled stochastic forward-backward infinite horizon integral equations. 510
12	Limit theorems for a one-dimensional system with random switchings Hurth, Tobias 15 November 2010 (has links) We consider a simple one-dimensional random dynamical system with two driving vector fields and random switchings between them. We show that this system satisfies a one force - one solution principle and compute its unique invariant density explicitly. We study the limiting behavior of the invariant density as the switching rate approaches zero and infinity and derive analogues of classical probabilistic results such as the central limit theorem and large deviations principle. One-dimensional random dynamical system Large deviations principle Central limit theorem Invariant density Driving vector fields One force - one solution principle Random switchings Limit theorems (Probability theory) Random dynamical systems

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Pathwise anticipating random periodic solutions of SDEs and SPDEs with linear multiplicative noise

Limit theorems for a one-dimensional system with random switchings