Coupling for some partial differential equations driven by white noise
نویسنده
چکیده
We prove, using coupling arguments, exponential convergence to equilibrium for reaction–diffusion and Burgers equations driven by space-time white noise. We use a coupling by reflection. 2000 Mathematics Subject Classification: 60H15, 35K57, 35Q53
منابع مشابه
Stochastic Partial Differential Equations Driven by Multi-parameter White Noise of Lévy Processes
We give a short introduction to the white noise theory for multiparameter Lévy processes and its application to stochastic partial differential equations driven by such processes. Examples include temperature distribution with a Lévy white noise heat source, and heat propagation with a multiplicative Lévy white noise heat source.
متن کاملExponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling
We consider parabolic stochastic partial differential equations driven by white noise in time. We prove exponential convergence of the transition probabilities towards a unique invariant measure under suitable conditions. These conditions amount essentially to the fact that the equation transmits the noise to all its determining modes. Several examples are investigated, including some where the...
متن کاملA Stabilization Phenomenon for a Class of Stochastic Partial Differential Equations
In this paper we investigate the long-time behavior of solutions to a class of semilinear, stochastic partial differential equations defined on a bounded domain D ⊂ R with smooth boundary ∂D and driven by an infinite-dimensional noise derived from an L(D)-valued Wiener process. We consider the case of a noise with nuclear covariance and we derive the almost sure convergence of solutions to one ...
متن کاملStochastic Partial Differential Equations Driven by Lévy Space - Time White Noise
In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Lévy white noise. As an example we use this theory to solve the stochastic Poisson equation with respect to Lévy white noise for any dimension d. The solution is a stochastic distribution process given explicitly. We also show that if d ≤ 3, then this s...
متن کاملar X iv : m at h / 01 09 11 5 v 1 [ m at h . PR ] 1 8 Se p 20 01 Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling
We consider parabolic stochastic partial differential equations driven by white noise in time. We prove exponential convergence of the transition probabilities towards a unique invariant measure under suitable conditions. These conditions amount essentially to the fact that the equation transmits the noise to all its determining modes. Several examples are investigated, including some where the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004