1. CMB 2010 (vol 53 pp. 526)
|On Some Stochastic Perturbations of Semilinear Evolution Equations|
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 ItÃ´ equation with locally Lipschitz nonlinearites. An example of the equation is given.
Keywords:evolution equation, mild solution, non-Lipschitz drift, Ito integral