On Some Stochastic Perturbations of Semilinear Evolution Equations

Canadian mathematical bulletin

Anna Milian¹ 

[1] Cracow University of Technology

关键词: evolution equation;    mild solution;    non-Lipschitz drift;    Ito integral;   

DOI  :  10.4153/CMB-2010-046-2

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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.

【 授权许可】

Unknown