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On Some Stochastic Perturbations of Semilinear Evolution Equations

  Published:2010-05-11
 Printed: Sep 2010
  • Anna Milian,
    Cracow University of Technology
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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.
Keywords: evolution equation, mild solution, non-Lipschitz drift, Ito integral evolution equation, mild solution, non-Lipschitz drift, Ito integral
MSC Classifications: 60H20 show english descriptions Stochastic integral equations 60H20 - Stochastic integral equations
 

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