Master's Thesis. Limit theorems for a one dimensional system with random switchings.

Dissertation Defense
Tuesday, October 5, 2010 - 3:05pm for 1 hour (actually 50 minutes)
Skiles 114
Tobias Hurth – School of Mathematics, Georgia Tech
Yuri Bakhtin
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 the unique invariant density explicitly. We study the limiting behavior of the invariant density as the switching rate approaches zero or infinity and derive analogues of classical probability theory results such as central limit theorem and large deviation principle.