ALMOST PERIODIC SOLUTIONS TO STOCHASTIC EVOLUTION EQUATIONS ON BANACH SPACES

作者：Crewe P^*

来源：Stochastics and Dynamics, 2013, 13(3): 1250027.

DOI：10.1142/S021949371250027X

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

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.

• 出版日期2013-9