TY - JOUR
ID - 609
TI - Stochastic differential inclusions of semimonotone type in Hilbert spaces
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Abedi, H.
AD - University of Kashan
Y1 - 2015
PY - 2015
VL - 41
IS - 2
SP - 291
EP - 306
KW - Stochastic differential inclusions
KW - Stochastic set-valued integrals
KW - Generalized solutions
KW - Semimonotone and hemicontinuous set-valued process
DO -
N2 - 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.]
UR - http://bims.iranjournals.ir/article_609.html
L1 - http://bims.iranjournals.ir/article_609_1f6207d995c810c1dfea87b7aad3943e.pdf
ER -