Menshikov, Mikhail V. and Vachkovskaia, M. and Wade, A.R. (2008) Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains. Journal of Statistical Physics, 132 (6). pp. 10971133. ISSN 00224715

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Abstract
We study stochastic billiards in infinite planar domains with curvilinear boundaries: that is, piecewise deterministic motion with randomness introduced via random reflections at the domain boundary. Physical motivation for the process originates with ideal gas models in the Knudsen regime, with particles reflecting off microscopically rough surfaces. We classify the process into recurrent and transient cases. We also give almostsure results on the longterm behaviour of the location of the particle, including a superdiffusive rate of escape in the transient case. A key step in obtaining our results is to relate our process to an instance of a onedimensional stochastic process with asymptotically zero drift, for which we prove some new almostsure bounds of independent interest. We obtain some of these bounds via an application of general semimartingale criteria, also of some independent interest.
Item type:  Article 

ID code:  13394 
Keywords:  stochastic billiards, rarefied gas dynamics, Knudsen random walk, random reflections, recurrence/transience, lamperti problem, almostsure bounds, birthanddeath chain, Probabilities. Mathematical statistics, Mathematics, Mathematical Physics, Statistical and Nonlinear Physics 
Subjects:  Science > Mathematics > Probabilities. Mathematical statistics Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Mrs Carolynne Westwood 
Date Deposited:  12 Nov 2009 13:44 
Last modified:  12 Dec 2015 05:23 
URI:  http://strathprints.strath.ac.uk/id/eprint/13394 
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