Geodesic
On Some Stochastic Perturbations of Semilinear Evolution Equations
Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 526-533

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DOI

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.
DOI : 10.4153/CMB-2010-046-2
Mots-clés : 60H20, evolution equation, mild solution, non-Lipschitz drift, Ito integral 
Milian, Anna. On Some Stochastic Perturbations of Semilinear Evolution Equations. Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 526-533. doi: 10.4153/CMB-2010-046-2
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     author = {Milian, Anna},
     title = {On {Some} {Stochastic} {Perturbations} of {Semilinear} {Evolution} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {526--533},
     year = {2010},
     volume = {53},
     number = {3},
     doi = {10.4153/CMB-2010-046-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-046-2/}
}
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