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Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains | | Mikhail V. Menshikov
; Marina Vachkovskaia
; Andrew R. Wade
; | | Date: |
13 Feb 2008 | | 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 almost-sure results on the
long-term behaviour of the location of the particle, including a
super-diffusive rate of escape in the transient case. A key step in obtaining
our results is to relate our process to an instance of a one-dimensional
stochastic process with asymptotically zero drift, for which we prove some new
almost-sure bounds of independent interest. We obtain some of these bounds via
an application of general semimartingale criteria, which are again of some
independent interest. | | Source: | arXiv, 0802.1865 | | Services: | Forum | Review | PDF | Favorites | |
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