ALMOST PERIODIC SOLUTIONS TO STOCHASTIC EVOLUTION EQUATIONS ON BANACH SPACES

被引：7

作者：

Crewe, P. ^{[1
]}

机构：

[1] Univ Oxford St Johns Coll, Oxford OX1 3JP, England

来源：

STOCHASTICS AND DYNAMICS | 2013年 / 13卷 / 03期

关键词：

Stochastic differential equations; almost periodicity; R-boundedness; evolution family; gamma-radonifying operators; INTEGRATION;

D O I：

10.1142/S021949371250027X

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 prove the existence of almost periodic solutions to a class of abstract stochastic evolution equations on a Banach space E, d X (t) = (A(t) X (t) + F(t))dt + G(t)dW (t), t is an element of R, Both autonomous (A is a C-0-semigroup generator) and non-autonomous (A (t) satisfies conditions of Acquistapace-Terreni and generates a strongly continuous evolution family) cases are studied. Results are based on the theory of stochastic integration on Banach spaces of van Neerven and Weis and R-boundedness estimates for semigroups and evolution families due to Hytonen and Veraar. An example is given for a non-autonomous second order boundary value problem on a domain in R-d.

引用

页数：23

共 21 条

[1]

Acquistapace P., 1987, Rend. Semin. Mat. Univ. Padova, V78, P47, DOI [10.1016/0022-1236(85)90050-3, DOI 10.1016/0022-1236(85)90050-3]

[2]

Acquistapace P., 1998, DIFFERENTIAL INTEGRA, V1, P433

[3]

[Anonymous], 2000, GRAD TEXT M

[4]

[Anonymous], 1995, ABSTRACT LINEAR THEO

[5] Almost Periodicity of Parabolic Evolution Equations with Inhomogeneous Boundary Values [J].