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.

引用

页码：582 / 602

页数：21

共 50 条

[1] ON RECURRENCE AND TRANSIENCE OF SOME LEVY-TYPE PROCESSES IN R
Knopova, Victoria
THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 2023, : 59 - 75
[2] ERGODICITY OF LEVY-TYPE PROCESSES
Sandric, Nikola
ESAIM-PROBABILITY AND STATISTICS, 2016, 20 : 154 - 177
[3] On recurrence and transience of two-dimensional Levy and Levy-type processes
Sandric, Nikola
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2016, 126 (02) : 414 - 438
[4] On transience of Levy-type processes
Sandric, Nikola
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC REPORTS, 2016, 88 (07): : 1012 - 1040
[5] PERIODIC HOMOGENIZATION OF NONSYMMETRIC LEVY-TYPE PROCESSES
Chen, Xin
Chen, Zhen-Qing
Kumagai, Takashi
Wang, Jian
ANNALS OF PROBABILITY, 2021, 49 (06) : 2874 - 2921
[6] Ergodic aspects of some Ornstein-Uhlenbeck type processes related to Levy processes
Bertoin, Jean
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2019, 129 (04) : 1443 - 1454
[7] Time change equations for Levy-type processes
Kruehner, Paul
Schnurr, Alexander
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2018, 128 (03) : 963 - 978
[8] Parametrix construction for certain Levy-type processes
Knopova, Victoria
Kulik, Alexei
RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2015, 23 (02) : 111 - 136
[9] A FAMILY OF DENSITY EXPANSIONS FOR LEVY-TYPE PROCESSES
Lorig, Matthew
Pagliarani, Stefano
Pascucci, Andrea
ANNALS OF APPLIED PROBABILITY, 2015, 25 (01) : 235 - 267
[10] Time regularity of Levy-type evolution in Hilbert spaces and of some α-stable processes
Bednorz, Witold
Glowienko, Grzegorz
Talarczyk, Anna
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2021, 26

← 1 2 3 4 5 →