TY - JOUR
ID - 751
TI - Continuous dependence on coefficients for stochastic evolution equations with multiplicative Levy Noise and monotone nonlinearity
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Salavati, E.
AU - Zangeneh, B.
AD - Department of
Mathematical Sciences, Sharif University of Technology, P.O. Box 11365-11155, Tehran, Iran.
Y1 - 2016
PY - 2016
VL - 42
IS - 1
SP - 175
EP - 194
KW - Stochasic evolution equations
KW - monotone nonlinearity
KW - stochastic convolution integrals
KW - L'evy processes
DO -
N2 - Semilinear stochastic evolution equations with multiplicative L'evy noise are considered. The drift term is assumed to be monotone nonlinear and with linear growth. Unlike other similar works, we do not impose coercivity conditions on coefficients. We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. As corollaries of the continuity result, we derive sufficient conditions for asymptotic stability of the solutions, we show that Yosida approximations converge to the solution and we prove that solutions have Markov property. Examples on stochastic partial differential equations and stochastic delay differential equations are provided to demonstrate the theory developed. The main tool in our study is an inequality which gives a pathwise bound for the norm of stochastic convolution integrals.
UR - http://bims.iranjournals.ir/article_751.html
L1 - http://bims.iranjournals.ir/article_751_180a88e9aeb9128f8fb07944be871064.pdf
ER -