Se p 20 09 Harnack Inequality and Applications for Stochastic Evolution Equations with Monotone Drifts ∗
نویسنده
چکیده
As a Generalization to [37] where the dimension-free Harnack inequality was established for stochastic porous media equations, this paper presents analogous results for a large class of stochastic evolution equations with general monotone drifts. Some ergodicity, compactness and contractivity properties are established for the associated transition semigroups. Moreover, the exponential convergence of the transition semigroups to invariant measure and the existence of a spectral gap are also derived. As examples, the main results are applied to many concrete SPDEs such as stochastic reaction-diffusion equations, stochastic porous media equations and the stochastic pLaplace equation in Hilbert space.
منابع مشابه
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 ...
متن کاملStochastic evolution equations with multiplicative Poisson noise and monotone nonlinearity
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 differentia...
متن کاملWeak differentiability of solutions to SDEs with semi-monotone drifts
In this work we prove Malliavin differentiability for the solution to an SDE with locally Lipschitz and semi-monotone drift. To prove this formula, we construct a sequence of SDEs with globally Lipschitz drifts and show that the $p$-moments of their Malliavin derivatives are uniformly bounded.
متن کاملThe Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity
We establish the Harnack inequality for advection-diffusion equations with divergencefree drifts of low regularity. While our previous work [IKR] considered the elliptic case, here we treat the more challenging parabolic problem by adapting the classical Moser technique to parabolic equations with drifts with regularity lower than the scale-invariant spaces.
متن کاملStochastic differential inclusions of semimonotone type in Hilbert spaces
In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...
متن کامل