Limit theorems for a one-dimensional system with random switchings

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.

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Georgia Institute of Technology

Year dc:date.issued

2010

Author dc:creator

• Hurth, Tobias

Advisor dc:contributor.advisor

• Bakhtin, Yuri

Committee members dc:contributor.committeemember

• Bunimovich, Leonid
• Koltchinskii, Vladimir

• One-dimensional random dynamical system
• Large deviations principle
• Central limit theorem
• Invariant density
• Driving vector fields
• One force - one solution principle
• Random switchings

Handle dc:identifier.uri

http://hdl.handle.net/1853/37201

OAI identifier oai:identifier

oai:repository.gatech.edu:1853/37201