Continuous dependence on coefficients for stochastic evolution equations with multiplicative Levy Noise and monotone nonlinearity

Abstract

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.