EVOLUTION EQUATIONS DRIVEN BY GENERAL STOCHASTIC MEASURES IN HILBERT SPACE

被引：17

作者：

Radchenko, V. M. ^{[1
]}

机构：

[1] Taras Shevchenko Natl Univ Kyiv, Kiev, Ukraine

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2015年 / 59卷 / 02期

关键词：

stochastic measure; stochastic integration in Hilbert space; stochastic evolution equation; mild solution; REGULARITY; VALUES;

D O I：

10.1137/S0040585X97T987119

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 stochastic evolution equations in Hilbert space driven by general stochastic measures. For stochastic measures in the equations we assume s-additivity in probability only. The integrals of deterministic functions with respect to stochastic measures in Hilbert space are defined. Existence and continuity of the mild solutions of the equations are proved.

引用

下载

页码：328 / U185

页数：12

共 50 条

[1] The regularity of fractional stochastic evolution equations in Hilbert space
Su, Xiaoyan
Li, Miao
STOCHASTIC ANALYSIS AND APPLICATIONS, 2018, 36 (04) : 639 - 653
[2] LINEAR STOCHASTIC EVOLUTION EQUATIONS IN HILBERT-SPACE
ICHIKAWA, A
JOURNAL OF DIFFERENTIAL EQUATIONS, 1978, 28 (02) : 266 - 277
[3] Approximate Controllability of Stochastic Degenerate Evolution Equations: Decomposition of a Hilbert Space
Ahmadova, Arzu
DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, 2023, 33 (1) : 355 - 377
[4] Relaxed solutions for stochastic evolution equations on Hilbert space with polynomial nonlinearities
Ahmed, NU
PUBLICATIONES MATHEMATICAE-DEBRECEN, 1999, 54 (1-2): : 75 - 101
[5] Adapted solutions of backward stochastic evolution equations with jumps on Hilbert space
Situ, R.
Xu, H.-Y.
2001, Journal of Zhongshan University (40):
[6] 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
[7] STOCHASTIC DIFFERENTIAL EQUATIONS IN HILBERT SPACE
CURTAIN, RF
FALB, PL
JOURNAL OF DIFFERENTIAL EQUATIONS, 1971, 10 (03) : 412 - &
[8] On time-dependent stochastic evolution equations driven by fractional Brownian motion in a Hilbert space with finite delay
Ren, Yong
Cheng, Xing
Sakthivel, Rathinasamy
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2014, 37 (14) : 2177 - 2184
[9] On dissipative stochastic equations in a Hilbert space
Holevo, AS
PROBABILITY THEORY AND RELATED FIELDS, 1996, 104 (04) : 483 - 500
[10] Stochastic Evolution Equations in Hilbert Spaces
Kruse, Raphael
STRONG AND WEAK APPROXIMATION OF SEMILINEAR STOCHASTIC EVOLUTION EQUATIONS, 2014, 2093 : 11 - 49

← 1 2 3 4 5 →