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Abedi, H. (2015). Stochastic differential inclusions of semimonotone type in Hilbert spaces. Bulletin of the Iranian Mathematical Society, 41(2), 291-306.
H. Abedi. "Stochastic differential inclusions of semimonotone type in Hilbert spaces". Bulletin of the Iranian Mathematical Society, 41, 2, 2015, 291-306.
Abedi, H. (2015). 'Stochastic differential inclusions of semimonotone type in Hilbert spaces', Bulletin of the Iranian Mathematical Society, 41(2), pp. 291-306.
Abedi, H. Stochastic differential inclusions of semimonotone type in Hilbert spaces. Bulletin of the Iranian Mathematical Society, 2015; 41(2): 291-306.

Stochastic differential inclusions of semimonotone type in Hilbert spaces

Article 2, Volume 41, Issue 2, April 2015, Page 291-306  XML PDF (178 K)
Document Type: Research Paper
Author
H. Abedi
University of Kashan
Receive Date: 10 March 2013,  Revise Date: 30 December 2013,  Accept Date: 19 January 2014 
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
Main Subjects
37-XX Dynamical systems and ergodic theory; 45-XX Integral equations; 60-XX Probability theory and stochastic processes
Statistics
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