@article {
author = {Abedi, H.},
title = {Stochastic differential inclusions of semimonotone type in Hilbert spaces},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {41},
number = {2},
pages = {291-306},
year = {2015},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) \in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It\^{o} stochastic integral of operator set-valued stochastic processes with respect to the cylindrical Brownian motion on separable Hilbert spaces. Then, we generalize the existence results for differential inclusions in [H. Abedi and R. Jahanipur, Nonlinear differential inclusions of semimonotone and condensing type in Hilbert spaces, \textit{Bull. Korean Math. Soc.}, {52} (2015), no. 2, 421--438.] to the corresponding stochastic differential inclusions using the methods discussed in [R. Jahanipur, Nonlinear functional differential equations of monotone-type in Hilbert spaces, {\it Nonlinear Analysis} {\bf 72} (2010), no. 3-4, 1393--1408, R. Jahanipur, Stability of stochastic delay evolution equations with monotone nonlinearity, {\it Stoch. Anal. Appl.}, {\bf 21} (2003), 161--181, and R. Jahanipur, Stochastic functional evolution equations with monotone nonlinearity: existence and stability of the mild solutions, {\it J. Differential Equations} {\bf 248} (2010), no. 5, 1230--1255.] },
keywords = {Stochastic differential inclusions,Stochastic set-valued integrals,Generalized solutions,Semimonotone and hemicontinuous set-valued process},
url = {http://bims.iranjournals.ir/article_609.html},
eprint = {http://bims.iranjournals.ir/article_609_1f6207d995c810c1dfea87b7aad3943e.pdf}
}