%0 Journal Article
%T Stochastic differential inclusions of semimonotone type in Hilbert spaces
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Abedi, H.
%D 2015
%\ 04/29/2015
%V 41
%N 2
%P 291-306
%! Stochastic differential inclusions of semimonotone type in Hilbert spaces
%K Stochastic differential inclusions
%K Stochastic set-valued integrals
%K Generalized solutions
%K Semimonotone and hemicontinuous set-valued process
%R
%X 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.]
%U http://bims.iranjournals.ir/article_609_1f6207d995c810c1dfea87b7aad3943e.pdf