Canad. Math. Bull. 53(2010), 526-533
Printed: Sep 2010
We consider semilinear evolution equations with some locally Lipschitz nonlinearities, perturbed by Banach space valued, continuous, and adapted stochastic process. We show that under some assumptions there exists a solution to the equation. Using the result we show that there exists a mild, continuous, global solution to a semilinear Itô equation with locally Lipschitz nonlinearites. An example of the equation is given.
evolution equation, mild solution, non-Lipschitz drift, Ito integral
60H20 - Stochastic integral equations