Almost Periodic Solutions For Stochastic Differential Equations

The thesis is dedicated to studying the problem of almost periodic solutions for semi-linear stochastic differential equation dx(t)=(Ax(t)+εF(t,x(t),ε))dt+εG(t,x(t),ε)dW(t)(*)with exponentially stable linear operator A and almost periodic in time coefficients F and G,where ￡ is a small positive real parameter.We prove that there is an ε0>0 such that for anyε∈[0,ε0]equation(*)admits at least one bounded solution which is continuous in ε in maximal norm,and furthermore this solution is almost periodic in distribution if the functions F and G are almost periodic.