Invariant measures of Lévy-type operators and their associated Markov processes

被引：0
作者：
Behme, Anita [1 ]
Oechsler, David [1 ]
机构：
[1] Tech Univ Dresden, Dresden, Germany
来源：
ELECTRONIC JOURNAL OF PROBABILITY | 2024年 / 29卷
关键词：
Feller processes; invariant distributions; L & eacute; vy-type operators; Markov processes; stochastic differential equations; Volterra-Fredholm integral equations; DRIVEN SDES; LEVY; ERGODICITY; EQUATIONS;
D O I：
10.1214/24-EJP1116
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：
A distributional equation as a criterion for invariant measures of Markov processes associated to L & eacute;vy-type operators is established. This is obtained via a characterization of infinitesimally invariant measures of the associated generators. Particular focus is put on the one-dimensional case where the distributional equation becomes a VolterraFredholm integral equation, and on solutions to L & eacute;vy-driven stochastic differential equations. The results are accompanied by various illustrative examples.
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页数：30
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