Martingale solutions and invariant measures for stochastic evolution equations in Banach spaces

被引：46

作者：

Brzezniak, Z ^{[1
]}

Gatarek, D

机构：

[1] Univ Hull, Dept Pure Math, Hull HU6 7RX, N Humberside, England

[2] Polish Acad Sci, Syst Res Inst, PL-01447 Warsaw 6, Poland

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1999年 / 84卷 / 02期

关键词：

(nonlinear) stochastic partial differential equations; stochastic integration in Banach spaces; dissipative mappings; martingale solutions; Feller processes; invariant measures;

D O I：

10.1016/S0304-4149(99)00034-4

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 paper we study the existence and uniqueness of weak solutions of stochastic differential equations on Banach spaces. We also study the existence of invariant measures for the corresponding Markovian semigroups. Our main tool is the factorization of stochastic convolutions. We close the paper with some examples. (C) 1999 Elsevier Science B.V. All rights reserved. MSG: Primary 60H15; 60G60; Secondary 60J25.

引用

页码：187 / 225

页数：39

共 50 条

[41] CONVERGENCE OF APPROXIMATE SOLUTIONS TO QUASILINEAR EVOLUTION EQUATIONS IN BANACH-SPACES
SANEKATA, N
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1979, 55 (07) : 245 - 249
[42] 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
[43] Martingale inequalities on rearrangement-invariant quasi-Banach function spaces
Ho K.-P.
Acta Scientiarum Mathematicarum, 2017, 83 (3-4): : 619 - 627
[44] VECTOR MEASURES APPLIED TO OPTIMAL CONTROL FOR A CLASS OF EVOLUTION EQUATIONS ON BANACH SPACES
Ahmed, Nasir Uddin
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2020, 35 (04): : 1329 - 1352
[45] WIENER-POISSON TYPE MULTIVALUED STOCHASTIC EVOLUTION EQUATIONS IN BANACH SPACES
Wu, Jing
STOCHASTICS AND DYNAMICS, 2012, 12 (02)
[46] On solutions of differential equations in Banach spaces
Cichon, M
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 60 (04) : 651 - 667
[47] Existence of invariant measures for diffusion processes on Banach spaces
Röckner, M
Zhang, TSS
SEMINAR ON STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS, 1999, 45 : 261 - 265
[48] EVOLUTION EQUATIONS AND SUBDIFFERENTIALS IN BANACH SPACES
Akagi, Goro
Otani, Mitsuharu
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2003, : 11 - 20
[49] NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES
TON, BA
JOURNAL OF DIFFERENTIAL EQUATIONS, 1971, 9 (03) : 608 - &
[50] Stochastic evolution equations in Banach spaces and applications to the Heath-Jarrow-Morton-Musiela equations
Brzezniak, Zdzislaw
Kok, Tayfun
FINANCE AND STOCHASTICS, 2018, 22 (04) : 959 - 1006

← 1 2 3 4 5 →