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Explicit Rates of Exponential Convergence for Reflected Jump-Diffusions on the Half-Line

Consider a reflected jump-diffusion on the positive half-line. Assume it is stochastically ordered. We apply the theory of Lyapunov functions and find explicit estimates for the rate of exponential convergence to the stationary distribution, as time goes to infinity. This continues the work of Lund, Meyn and Tweedie (1996). We apply these results to systems of two competing Levy particles with rank-dependent dynamics.