A criterion for invariant measures of Ito processes based on the symbol

被引：7

作者：

Behme, Anita ^{[1
,2
]}

Schnurr, Alexander ^{[3
,4
]}

机构：

[1] Tech Univ Dresden, Inst Math Stochast, D-01062 Dresden, Germany

[2] Tech Univ Munich, Ctr Math Sci, D-85748 Garching, Germany

[3] Univ Siegen, Dept Math, D-57072 Siegen, Germany

[4] Tech Univ Dortmund, Lehrstuhl 4, Fak Math, D-44227 Dortmund, Germany

来源：

BERNOULLI | 2015年 / 21卷 / 03期

关键词：

Feller process; invariant measure; Ito process; Levy-type process; stationarity; stochastic differential equation; symbol; FELLER; STATIONARITY; EQUATIONS;

D O I：

10.3150/14-BEJ618

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：

An integral criterion for the existence of an invariant measure of an Ito process is developed. This new criterion is based on the probabilistic symbol of the Ito process. In contrast to the standard integral criterion for invariant measures of Markov processes based on the generator, no test functions and hence no information on the domain of the generator is needed.

引用

页码：1697 / 1718

页数：22

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