Stochastic billiards in unbounded planar domains
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Mon, 16/02/2009 15:45 |
Dr Andrew Wade (Bristol) |
Stochastic Analysis Seminar  |
Oxford-Man Institute |
| Motivated by ideal gas models in the low density regime, we study a randomly reflecting particle travelling at constant speed in an unbounded domain in the plane with boundary satisfying a polynomial growth condition The growth rate of the domain, together with the reflection distribution, determine the asymptotic behaviour of the process. We give results on recurrence vs. transience, and on almost-sure-bounds for the particle including the rate of escape in the transient case. The proofs exploit a surprising relationship with Lamperti's problem of a process on the half-line with asymptotically zero drift. This is joint work with Mikhail Menshikov and Marina Vachkovskaia. | |||