Reflected Brownian Motion in a Convex Polyhedral Cone: Tail Estimates for the Stationary Distribution

Andrey Sarantsev ()
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Andrey Sarantsev: University of California, Santa Barbara

Journal of Theoretical Probability, 2017, vol. 30, issue 3, 1200-1223

Abstract: Abstract Consider a multidimensional obliquely reflected Brownian motion in the positive orthant, or, more generally, in a convex polyhedral cone. We find sufficient conditions for existence of a stationary distribution and convergence to this distribution at an exponential rate, as time goes to infinity, complementing the results of Dupuis and Williams (Ann Probab 22(2):680–702, 1994) and Atar et al. (Ann Probab 29(2):979–1000, 2001). We also prove that certain exponential moments for this distribution are finite, thus providing a tail estimate for this distribution. Finally, we apply these results to systems of rank-based competing Brownian particles, introduced in Banner et al. (Ann Appl Probab 15(4):2296–2330, 2005).

Keywords: Reflected Brownian motion; Lyapunov function; Tail estimate; Generator; Convex polyhedron; Polyhedral cone; Competing Brownian particles; Symmetric collisions; Gap process; Primary 60J60; Secondary 60J55; 60J65; 60H10; 60K35 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10959-016-0674-8

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