共查询到20条相似文献,搜索用时 46 毫秒
1.
Ruisheng Qi Xiaoyuan Yang Yinghan Zhang 《Numerical Methods for Partial Differential Equations》2013,29(6):1946-1962
We study the full‐discrete finite element method for the stochastic elastic equation driven by additive noise. To analyze the error estimates, we write the stochastic elastic equation as an abstract stochastic equation. Strong convergence estimates in the root mean square L2 ‐norm are obtained by using the error estimates for the deterministic problem and the semigroup theory. Numerical experiments are carried out to verify the theoretical results. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
2.
In this paper, we consider the ergodicity of invariant measures for the stochastic Ginzburg-Landau equation with degenerate random forcing. First, we show the existence and pathwise uniqueness of strong solutions with H1-initial data, and then the existence of an invariant measure for the Feller semigroup by the Krylov-Bogoliubov method. Then in the case of degenerate additive noise, using the notion of asymptotically strong Feller property, we prove the uniqueness of invariant measures for the transition semigroup. 相似文献
3.
This paper investigates a damped stochastic wave equation driven by a non-Gaussian Lévy noise. The weak solution is proved
to exist and be unique. Moreover we show the existence of a unique invariant measure associated with the transition semigroup
under mild conditions. 相似文献
4.
m-Dissipativity for Kolmogorov Operator of a Fractional Burgers Equation with Space-time White Noise
Desheng Yang 《Potential Analysis》2016,44(2):215-227
This paper is concerned with the essential m-dissipativity of the Kolmogorov operator associated with a fractional stochastic Burgers equation with space-time white noise. Some estimates on the solution and its moments with respect to the invariant measure are given. Moreover we also study the smoothing properties of the transition semigroup and the corresponding fractional Ornstein-Uhlenbeck operator by introducing an auxiliary semigroup and (generalized) Bismut-Elworthy formula. From these results, we prove that the Kolmogorov operator of the problem is m-dissipative and the domain of the infinitesimal generator of the fractional Ornstein-Uhlenbeck operator is a core. 相似文献
5.
Bin Xie 《Potential Analysis》2012,36(1):35-66
In this paper, we are attempting to study the uniqueness of invariant measures of a stochastic differential equation driven
by a Lévy type noise in a real separable Hilbert space. To investigate this problem, we study the strong Feller property and
irreducibility of the corresponding Markov transition semigroup respectively. To show the strong Feller property, we generalize
a Bismut–Elworthy–Li type formula to our Markov transition semigroup under a non-degeneracy condition of the coefficient of
the Wiener process. 相似文献
6.
Joris Bierkens Onno van Gaans Sjoerd Verduyn Lunel 《Journal of Evolution Equations》2009,9(4):771-786
It is shown that for an SDE in a Hilbert space, eventual compactness of the driving semigroup together with compact perturbations
can be used to establish the existence of an invariant measure. The result is applied to stochastic functional differential
equations and the heat equation perturbed by delay and noise, which are both shown to be driven by an eventually compact semigroup. 相似文献
7.
Luigi Manca 《Potential Analysis》2010,32(1):67-99
We are concerned with a viscous Burgers equation forced by a perturbation of white noise type. We study the corresponding
transition semigroup in a space of continuous functions weighted by a proper potential, and we show that the infinitesimal
generator is the closure (with respect to a suitable topology) of the Kolmogorov operator associated to the stochastic equation.
In the last part of the paper we use this result to solve the corresponding Fokker-Planck equation. 相似文献
8.
Luigi Manca 《Journal of Evolution Equations》2008,8(2):231-262
We consider a semigroup of operators in the Banach space C
b
(H) of uniformly continuous and bounded functions on a separable Hilbert space H. We prove an existence and uniqueness result for a measure valued equation involving this class of semigroups. Then we apply
the result to the transition semigroup and the Kolmogorov operator corresponding to a stochastic PDE in H. For this purpose, we characterize the generator of the transition semigroup on a core.
相似文献
9.
A variational approach to stochastic nonlinear diffusion problems with dynamical boundary conditions
We study a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise; we allow stochastic boundary conditions that depend on the time derivative of the solution on the boundary. This work provides the existence and uniqueness of the solution and it shows the existence of an ergodic invariant measure for the corresponding transition semigroup; furthermore, under suitable additional assumptions, uniqueness and strong asymptotic stability of the invariant measure are proved. 相似文献
10.
The main object of study is the stochastic Cauchy problem for a quasilinear equation with random disturbances in the form of a Hilbert-valued white noise process and with an operator generating an integrated semigroup in the space L2(R). We use the Colombeau theory of multiplication of distributions to introduce an abstract stochastic factor algebra and construct an approximate solution of the problem in this algebra. 相似文献
11.
Ruth F. Curtain 《Journal of Mathematical Analysis and Applications》1977,60(3):570-595
Existence and uniqueness theorems are proved for a general class of stochastic linear abstract evolution equations, with a general type of stochastic forcing term. The abstract evolution equation is modeled using an evolution operator (or 2-parameter semigroup) approach and this includes linear partial differential equations and linear differential delay equations. The stochastic forcing term is modeled by defining an Itô stochastic integral with respect to a Hilbert space-valued orthogonal increments process, which can be used to model both Gaussian and non-Gaussian white noise processes. The theory is illustrated by examples of stochastic partial differential equations and delay equations, which arise in filtering problems for distributed and delay systems. 相似文献
12.
Nikolai Chemetov Fernanda Cipriano 《Stochastic Processes and their Applications》2018,128(8):2710-2749
This article deals with a stochastic control problem for certain fluids of non-Newtonian type. More precisely, the state equation is given by the two-dimensional stochastic second grade fluids perturbed by a multiplicative white noise. The control acts through an external stochastic force and we search for a control that minimizes a cost functional. We show that the Gâteaux derivative of the control to state map is a stochastic process being the unique solution of the stochastic linearized state equation. The well-posedness of the corresponding stochastic backward adjoint equation is also established, allowing to derive the first order optimality condition. 相似文献
13.
In this paper, we prove the existence of a unique strong solution to a stochastic tamed 3D Navier–Stokes equation in the whole space as well as in the periodic boundary case. Then, we also study the Feller property of solutions, and prove the existence of invariant measures for the corresponding Feller semigroup in the case of periodic conditions. Moreover, in the case of periodic boundary and degenerated additive noise, using the notion of asymptotic strong Feller property proposed by Hairer and Mattingly (Ann. Math. 164:993–1032, 2006), we prove the uniqueness of invariant measures for the corresponding transition semigroup. 相似文献
14.
Peter Kotelenez 《Stochastic Processes and their Applications》1984,17(1):115-125
Necessary and sufficient conditions for Hölder continuity of Hilbert space valued martingales are given in terms of the associated quadratic variation. As an application one obtains a sufficient condition for a mild solution of a stochastic evolution equation to have a continuous version if the semigroup governing this equation is analytic. Further we derive Levy's modulus of continuity for the Hilbert space valued stochastic integral with the Wiener process as integrator and obtain a generalization of the loglog law for that integral. 相似文献
15.
Wei LIU 《Frontiers of Mathematics in China》2011,6(3):449-472
In this paper, we first show the uniqueness of invariant measures for the stochastic fast diffusion equation, which follows
from an obtained new decay estimate. Then we establish the Harnack inequality for the stochastic fast diffusion equation with
nonlinear perturbation in the drift and derive the heat kernel estimate and ultrabounded property for the associated transition
semigroup. Moreover, the exponential ergodicity and the existence of a spectral gap are also investigated. 相似文献
16.
We solve a control problem for the stochastic Burgers equation using the dynamic programming approach. The cost functional
involves exponentially growing functions and the analog of the kinetic energy; the case of a distributed parameter control
is considered. The Hamilton-Jacobi equation is solved by a compactness method and a-priori estimates are obtained thanks to
the regularizing properties of the transition semigroup associated to the stochastic Burgers equation; a fixed point argument
does not seem to apply here.
Entrata in Redazione il 10 dicembre 1998. 相似文献
17.
We consider a stochastic partial differential equation with logarithmic (or negative power) nonlinearity, with one reflection at 0 and with a constraint of conservation of the space average. The equation, driven by the derivative in space of a space–time white noise, contains a bi-Laplacian in the drift. The lack of the maximum principle for the bi-Laplacian generates difficulties for the classical penalization method, which uses a crucial monotonicity property. Being inspired by the works of Debussche and Zambotti, we use a method based on infinite dimensional equations, approximation by regular equations and convergence of the approximated semigroup. We obtain existence and uniqueness of a solution for nonnegative initial conditions, results on the invariant measures, and on the reflection measures. 相似文献
18.
It is shown that transition measures of the stochastic Navier-Stokes equation in 2D converge exponentially fast to the corresponding invariant measures in the distance of total variation. As a corollary we obtain the existence of spectral gap for a related semigroup obtained by a sort of ground state transformation. Analogous results are proved for the stochastic Burgers equation. 相似文献
19.
In this work we construct a Markov family of martingale solutions for 3D stochastic Navier–Stokes equations (SNSE) perturbed by Lévy noise with periodic boundary conditions. Using the Kolmogorov equations of integrodifferential type associated with the SNSE perturbed by Lévy noise, we construct a transition semigroup and establish the existence of a unique invariant measure. We also show that it is ergodic and strongly mixing. 相似文献
20.
《Journal de Mathématiques Pures et Appliquées》2003,82(8):877-947
We consider the Kolmogorov equation associated with the stochastic Navier–Stokes equations in 3D, we prove existence of a solution in the strict or mild sense. The method consists in finding several estimates for the solutions um of the Galerkin approximations of u and their derivatives. These estimates are obtained with the help of an auxiliary Kolmogorov equation with a very irregular negative potential. Although uniqueness is not proved, we are able to construct a transition semigroup for the 3D Navier–Stokes equations. Furthermore, this transition semigroup has a unique invariant measure, which is ergodic and strongly mixing. 相似文献