Wiener chaos solutions of linear stochastic evolution equations
نویسندگان
چکیده
منابع مشابه
Stochastic Differential Equations: a Wiener Chaos Approach
A new method is described for constructing a generalized solution for stochastic differential equations. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and provides a unified framework for the study of ordinary and partial differential equations driven by finiteor infinite-dimensional noise with either adapted or anticipating input. Existence, uniqueness, regula...
متن کاملLinear Parabolic Stochastic PDE's and Wiener Chaos
We study Cauchy’s problem for a second-order linear parabolic stochastic partial differential equation (SPDE) driven by a cylindrical Brownian motion. Existence and uniqueness of a generalized (soft) solution is established in Sobolev, Hölder, and Lipschitz classes. We make only minimal assumptions, virtually identical to those common to similar deterministic problems. A stochastic Feynman–Kac ...
متن کاملWiener Chaos Expansion and Numerical Solutions of Stochastic Partial Differential Equations
xv
متن کاملThe Wiener-Askey Polynomial Chaos for Stochastic Differential Equations
We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener’s polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error. Several continuous and disc...
متن کاملWiener Chaos Versus Stochastic Collocation Methods for Linear Advection-Diffusion-Reaction Equations with Multiplicative White Noise
We compare Wiener chaos and stochastic collocation methods for linear advectionreaction-diffusion equations with multiplicative white noise. Both methods are constructed based on a recursive multistage algorithm for long-time integration. We derive error estimates for both methods and compare their numerical performance. Numerical results confirm that the recursive multistage stochastic colloca...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2006
ISSN: 0091-1798
DOI: 10.1214/009117905000000738