2013/04/08 by Erfan Salavati, Salavati, Erfan, Bijan Z. Zangeneh +1
Economics, Econometrics and Finance · Mathematics · Social Sciences · #47H05 #47J35 #60G51 #60H10 #60H15 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1304.2122
openalex publication_date 2013/04/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Semilinear stochastic evolution equations with multiplicative Lévy noise and monotone nonlinear drift are considered. Unlike other similar work we do not impose coercivity conditions on coefficients. Existence and uniqueness of the mild solution is proved using an iterative method. The continuity of the solution with respect to initial conditions and coefficients is proved and a sufficient condition for exponential asymptotic stability of the solutions has been derived. The solutions are proved to have a Markov property. Examples on stochastic partial differential equations and stochastic delay equations are provided to demonstrate the theory developed. The main tool in our study is an Itô type inequality which gives a pathwise bound for the norm of stochastic convolution integrals.