Stochastic evolution equations with multiplicative Poisson noise and monotone nonlinearity
Authors
Abstract:
Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are considered. The coefficients are assumed to have linear growth. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and uniqueness of the mild solution is proposed. Examples on stochastic partial differential equations and stochastic delay differential equations are provided to demonstrate the theory developed.
similar resources
Continuous dependence on coefficients for stochastic evolution equations with multiplicative Levy Noise and monotone nonlinearity
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 ...
full textcontinuous dependence on coefficients for stochastic evolution equations with multiplicative l'evy noise and monotone nonlinearity
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 ...
full textcontinuous dependence on coefficients for stochastic evolution equations with multiplicative levy noise and monotone nonlinearity
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 corollarie...
full textErgodicity for Nonlinear Stochastic Evolution Equations with Multiplicative Poisson Noise
Abstract. We study the asymptotic behavior of solutions to stochastic evolution equations with monotone drift and multiplicative Poisson noise in the variational setting, thus covering a large class of (fully) nonlinear partial differential equations perturbed by jump noise. In particular, we provide sufficient conditions for the existence, ergodicity, and uniqueness of invariant measures. Furt...
full textStochastic evolution equations with multiplicative noise
We study parabolic stochastic partial differential equations (SPDEs), driven by two types of operators: one linear closed operator generating a C0−semigroup and one linear bounded operator with Wick-type multiplication, all of them set in the infinite dimensional space framework of white noise analysis. We prove existence and uniqueness of solutions for this class of SPDEs. In particular, we al...
full textLarge Deviations for Stochastic Evolution Equations with Small Multiplicative Noise
The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. Roughly speaking, besides the assumptions for existence and uniqueness of the solution, one only need assume some additional assumptions on diffusion coefficient in order to obtain Large deviation principle for the dis...
full textMy Resources
Journal title
volume 43 issue 5
pages 1287- 1299
publication date 2017-10-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023