2015/09/06 by Andrey Sarantsev, Sarantsev, Andrey
Economics, Econometrics and Finance · Mathematics · #60H10 #60J55 #60J60 (Primary) #60J65 #60K35 (Secondary) #FOS: Mathematics #Financial Risk and Volatility Modeling #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60H10 #msc:60J55 #msc:60J60 #msc:60J65 #msc:60K35
paper · pdf · doi:10.48550/arxiv.1509.01781
18 pages. Keywords: reflected Brownian motion, Lyapunov function, tail estimate, generator, convex polyhedron, polyhedral cone, competing Brownian particles, symmetric collisions, gap process
openalex publication_date 2015/09/06 · arxiv created 2016/04/01 · arxiv updated 2016/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider an 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 the exponential rate, as time goes to infinity. 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.