Andrey Sarantsev
Published 2015-09-06Version 1
For a multidimensional jump-diffusion process, we construct a Lyapunov function and prove its exponential ergodicity. We do the same for obliquely reflected jump-diffusion processes in the positive orthant, extending results of Atar, Budhiraja and Dupuis (2001). We apply these results to systems of competing L\'evy particles, introduced in Shkolnikov (2011).
Comments: 26 pages. Keywords: Jump-diffusion processes, reflected diffusions, oblique reflection, positive orthant, reflected jump-diffusions, Lyapunov function, uniform ergodicity, tail estimate, stationary distribution, stochastic ordering, jump measures, competing Levy particles, gap process. arXiv admin note: text overlap with arXiv:1509.01781
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