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1	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