具有位置依赖跳跃速率的多维跳跃扩散的遍历性

IF 1.2 2区 数学 Q2 STATISTICS & PROBABILITY
E. Löcherbach, V. Rabiet
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引用次数: 6

摘要

我们考虑一个跳跃型扩散X = (Xt),它具有由Lψ(X) = 1/2∑a ij (X)∂2 ψ(X)/∂X i∂X j + g(X)∇ψ(X) +∫(ψ(X + c(z, X)) - ψ(X))γ(z, X)µ(dz)给出的无穷小发生器,其中µ具有无限的总质量。我们用一种完全基于过程跳跃的再生方案证明了X的Harris递推式。此外,对于可积加性泛函,我们用过程的系数陈述了允许用偏差不等式控制收敛到平衡的速度的显式条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Ergodicity for multidimensional jump diffusions with position dependent jump rate
We consider a jump type diffusion X = (Xt) with infinitesimal generator given by Lψ(x) = 1/2 ∑ a ij (x) ∂2 ψ(x)/∂x i ∂x j + g(x)∇ψ(x) + ∫ (ψ(x + c(z, x)) − ψ(x))γ(z, x)µ(dz) where µ is of infinite total mass. We prove Harris recurrence of X using a regeneration scheme which is entirely based on the jumps of the process. Moreover we state explicit conditions in terms of the coefficients of the process allowing to control the speed of convergence to equilibrium in terms of deviation inequalities for integrable additive functionals.
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来源期刊
CiteScore
2.70
自引率
0.00%
发文量
85
审稿时长
6-12 weeks
期刊介绍: The Probability and Statistics section of the Annales de l’Institut Henri Poincaré is an international journal which publishes high quality research papers. The journal deals with all aspects of modern probability theory and mathematical statistics, as well as with their applications.
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