On Ergodic Properties of Some Levy-Type Processes

被引：1
|
作者：
Knopova, Victoria [1 ]
Mokanu, Yana [1 ]
机构：
[1] Kiev T Shevchenko Univ, Dept Mech & Math, Glushkov Ave, UA-02000 Kiev, Ukraine
来源：
JOURNAL OF THEORETICAL PROBABILITY | 2024年 / 37卷 / 01期
关键词：
Ergodicity; Levy-type process; Foster-Lyapunov criteria; Lyapunov function; TRANSITION-PROBABILITY DENSITY; MARKOVIAN PROCESSES; SUBGEOMETRIC RATES; FELLER SEMIGROUPS; OPERATORS; DRIVEN; CONSTRUCTION; CONVERGENCE; STABILITY; BEHAVIOR;
D O I：
10.1007/s10959-023-01252-x
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：
In this note we find sufficient conditions for ergodicity of a Levy-type process withthe generator of the corresponding semigroup given byLf(x)=a(x)f'(x)+?(R)(f(x+u)-f(x)-?f(x).u1|u|=1)?(x,du),f?C-8(2)(R).Here ?(x,du) is a Levy-type kernel and a(.):R?R. We consider the case where the tails of?(x,.)have polynomial decay, as well as the case where the decay is(sub)-exponential. We use the Foster-Lyapunov approach to prove the results.
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页码：582 / 602
页数：21
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