On exponential stability of mild solutions for some stochastic partial integrodifferential equations

In this work, we study the existence and exponentially stability in p-mean square for some stochastic integrodifferential equation with delays. Also pathwise exponential stability is proved for p>2. We assume that the linear part has a resolvent operator in the sense given by Grimmer (1982). The delayed part is assumed to be continuous. Our results are proved by using the stochastic convolution.