Continuous dependence on coefficients for stochastic evolution equations with multiplicative L\'evy Noise and monotone nonlinearity

Semilinear stochastic evolution equations with multiplicative Levy noise are consideredý. ýThe drift term is assumed to be monotone nonlinear and with linear growthý. ýUnlike other similar worksý, ýwe do not impose coercivity conditions on coefficientsý. ýWe establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ýAs corollaries of the continuity resultý, ýwe derive sufficient conditions for asymptotic stability of the solutionsý, ýwe show that Yosida approximations converge to the solution and we prove that solutions have Markov propertyý. ýExamples on stochastic partial differential equations and stochastic delay differential equations are provided to demonstrate the theory developedý. ýThe main tool in our study is an inequality which gives a pathwise bound for the norm of stochastic convolution integralsý.