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On Some Stochastic Perturbations of Semilinear Evolution Equations

Published online by Cambridge University Press:  20 November 2018

Anna Milian
Anna Milian*
Affiliation:
Cracow University of Technology e-mail: milian@usk.pk.edu.pl
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Abstract

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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

60H20evolution equationmild solutionnon-Lipschitz driftIto integral
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 3 , 01 September 2010 , pp. 526 - 533
Copyright
Copyright © Canadian Mathematical Society 2010

References

[1] Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences 44, Springer-Verlag, New York, 1983.Google Scholar
[2] Prato, G. Da and Zabczyk, J., Stochastic Equations in Infinite Dimensions. Encyclopedia of Mathematics and its Applications 44. Cambridge University Press, 1992.Google Scholar