In this paper, we study existence and exponential stability problems of mild solutions associated with stochastic delay evolution equations in Hilbert spaces. These problems are resolved using the properties of a stochastic convolution integral and a comparison principle by exploiting Holder-type conditions on the drift and diffusion terms. The results obtained here generalize the corresponding main results from [1, 3, 4, 9, 13, 16].
T.E. Govindan. "On stochastic delay evolution equations with non-lipschitz nonlinearities in Hilbert spaces." Differential Integral Equations 22 (1/2) 157 - 176, January/February 2009. https://doi.org/10.57262/die/1356038559