Spinning Brownian motion

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1 Citation (Scopus)


We prove strong existence and uniqueness for a reflection process X in a smooth, bounded domain D that behaves like obliquely-reflected-Brownian-motion, except that the direction of reflection depends on a (spin) parameter S, which only changes when X is on the boundary of D according to a physical rule. The process (X,S) is a degenerate diffusion. We show uniqueness of the stationary distribution by using techniques based on excursions of X from ∂D, and an associated exit system. We also show that the process admits a submartingale formulation and use related results to show examples of the stationary distribution.

Original languageEnglish
Pages (from-to)4178-4203
Number of pages26
JournalStochastic Processes and their Applications
Issue number11
Publication statusPublished - 1 Nov 2015


  • Degenerate reflected diffusion
  • Excursion theory
  • Stationary distribution
  • Stochastic differential equations

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics


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