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- W91547916 abstract "We consider semimartingale reflected Brownian motion in the positive orthant. In the interior of the orthant, it behaves as a Brownian motion with a constant drift vector and a constant covariance matrix. On each of the faces of the boundary, it is reflected in a certain direction, constant on this face. The reflection may be not normal, but oblique. Under certain conditions, it has a unique stationary distribution and converges to it exponentially fast. We provide several explicit estimates for the exponential rate of convergence. We find an explicit tail estimate for the stationary distribution. We introduce a version of this process which has jumps and show similar results for this new process. Our main tool is the theory of Lyapunov function. In addition, we use some new results on stochastic comparison and stochastic ordering of reflected Brownian motion in the orthant, which we also prove in this article. We apply these results to systems of competing Brownian particles, including the case of asymmetric collisions, as well as systems of competing Levy particles." @default.
- W91547916 created "2016-06-24" @default.
- W91547916 creator A5035530377 @default.
- W91547916 date "2013-05-07" @default.
- W91547916 modified "2023-09-27" @default.
- W91547916 title "Explicit Rates of Exponential Convergence for Reflected Brownian Motion in the Orthant" @default.
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- W91547916 hasPublicationYear "2013" @default.
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