Invariant measures and a stability theorem for locally Lipschitz stochastic delay equations

被引：0

作者：

Stojkovic, I. ^{[1
]}

van Gaans, O. ^{[1
]}

机构：

[1] Leiden Univ, Math Inst, NL-2300 RA Leiden, Netherlands

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2011年 / 47卷 / 04期

关键词：

Delay equation; Invariant measure; Levy process; Semimartingale; Skorohod space; Stability; Tightness; Variation-of-constants formula; FUNCTIONAL-DIFFERENTIAL EQUATIONS; COEFFICIENTS; DRIVEN; UNIQUENESS; SYSTEMS; SPDES;

D O I：

10.1214/10-AIHP396

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 stochastic delay differential equation with exponentially stable drift and diffusion driven by a general Levy process. The diffusion coefficient is assumed to be locally Lipschitz and bounded. Under a mild condition on the large jumps of the Levy process, we show existence of an invariant measure. Main tools in our proof are a variation-of-constants formula and a stability theorem in our context, which are of independent interest.

引用

页码：1121 / 1146

页数：26

共 50 条

[1] On implicit function theorem for locally Lipschitz equations
Arutyunov, Aram, V
Zhukovskiy, Sergey E.
MATHEMATICAL PROGRAMMING, 2023, 198 (01) : 1107 - 1120
[2] On implicit function theorem for locally Lipschitz equations
Aram V. Arutyunov
Sergey E. Zhukovskiy
Mathematical Programming, 2023, 198 : 1107 - 1120
[3] Invariant measures of stochastic delay complex Ginzburg-Landau equations
Ren, Die
Shu, Ji
Liu, Aili
Zou, Yanyan
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2024, 96 (06) : 1667 - 1699
[4] STABILITY THEOREM OF SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS UNDER LOCALIZED LIPSCHITZ CONDITIONS
吴让泉
冯玉瑚
ScienceBulletin, 1988, (10) : 812 - 815
[5] Stochastic partial functional differential equations with locally monotone coefficients, locally Lipschitz non-linearity and delay
Lv, Guangying
Pang, Peter Y. H.
APPLICABLE ANALYSIS, 2017, 96 (16) : 2737 - 2757
[6] Invariant Measures of Stochastic Lattice Plate Equations: Stability, Ergodicity and Mixing
Wang, Yu
Yang, Congli
Wang, Renhai
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2024, 47 (03)
[7] Invariant measures and random attractors of stochastic delay differential equations in Hilbert space
Li, Shangzhi
Guo, Shangjiang
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2022, (56) : 1 - 25
[8] Invariant Measures for Stochastic Differential Equations
Hong, Jialin
Wang, Xu
INVARIANT MEASURES FOR STOCHASTIC NONLINEAR SCHRODINGER EQUATIONS: NUMERICAL APPROXIMATIONS AND SYMPLECTIC STRUCTURES, 2019, 2251 : 31 - 61
[9] Backward stochastic differential equations with locally Lipschitz coefficient
Bahlali, K
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 333 (05): : 481 - 486
[10] INVARIANT MEASURES OF STOCHASTIC DELAY LATTICE SYSTEMS
Chen, Zhang
Li, Xiliang
Wang, Bixiang
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2021, 26 (06): : 3235 - 3269

← 1 2 3 4 5 →