Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42120160201Continuous dependence on coefficients for stochastic evolution equations with multiplicative Levy Noise and monotone nonlinearity175194751ENE.SalavatiDepartment of
Mathematical Sciences, Sharif University of Technology, P.O. Box 11365-11155, Tehran, Iran.B.ZangenehDepartment of
Mathematical Sciences, Sharif University of Technology, P.O. Box 11365-11155, Tehran, Iran.Journal Article20140607Semilinear 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.http://bims.iranjournals.ir/article_751_180a88e9aeb9128f8fb07944be871064.pdf