Convergence to Equilibrium for Time-Inhomogeneous Jump Diffusions with State-Dependent Jump Intensity

被引：3
|
作者：
Locherbach, E. [1 ]
机构：
[1] Univ Paris 1 Pantheon Sorbonne, SAMM, 90 Rue Tolbiac, F-75013 Paris, France
来源：
JOURNAL OF THEORETICAL PROBABILITY | 2020年 / 33卷 / 04期
关键词：
Diffusions with position-dependent jumps; Nummelin splitting; Total variation coupling; Continuous-time Markov processes; Convergence to equilibrium; Asymptotic pseudotrajectories; NONPARAMETRIC-ESTIMATION; EXPONENTIAL ERGODICITY; LIMIT-THEOREMS; STABILITY; EQUATIONS; REGULARITY; SYSTEMS; SDES;
D O I：
10.1007/s10959-019-00947-4
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We consider a time-inhomogeneous Markov process X=(Xt)t and we are interested in its longtime behavior. The infinitesimal generator of the process is given for any sufficiently smooth test function f by Ltf(x)= n-ary sumation i=1d partial differential f partial differential xi(x)bi(t,x); Rm[f(x+c(t,z,x))-f(x)]gamma(t,z,x)mu(dz), Moreover, we introduce a coupling method for the limit process which is entirely based on certain of its big jumps and which relies on the regeneration method. We state explicit conditions in terms of the coefficients of the process allowing control of the speed of convergence to equilibrium both for X and for X over bar (X) over bar.
引用
收藏
页码：2280 / 2314
页数：35
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