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On Some Stochastic Perturbations of Semilinear Evolution Equations
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2010