Chaos Expansion of 2d Parabolic Anderson Model

نویسندگان

  • YU GU
  • JINGYU HUANG
چکیده

We prove a chaos expansion for the 2D parabolic Anderson Model in small time, with the expansion coefficients expressed in terms of the density function of the annealed polymer in a white noise environment.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Moments of 2d Parabolic Anderson Model

In this note, we use the Feynman-Kac formula to derive a moment representation for the 2D parabolic Anderson model in small time, which is related to the intersection local time of planar Brownian motions.

متن کامل

ar X iv : 0 70 6 . 23 90 v 1 [ m at h . PR ] 1 6 Ju n 20 07 STOCHASTIC PARABOLIC EQUATIONS OF FULL SECOND ORDER

A procedure is described for defining a generalized solution for stochastic differential equations using the Cameron-Martin version of the Wiener Chaos expansion. Existence and uniqueness of this Wiener Chaos solution is established for parabolic stochastic PDEs such that both the drift and the diffusion operators are of the second order.

متن کامل

Linear 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 کامل

Weak and almost sure limits for the parabolic Anderson model with heavy tailed potentials

We study the parabolic Anderson problem, i.e., the heat equation ∂tu = ∆u + ξu on (0,∞) × Z d with independent identically distributed random potential {ξ(z) : z ∈ Z} and localised initial condition u(0, x) = 10(x). Our interest is in the long-term behaviour of the random total mass U(t) = Pz u(t, z) of the unique non-negative solution in the case that the distribution of ξ(0) is heavy tailed. ...

متن کامل

Weak and Almost Sure Limits for the Parabolic Anderson Model with Heavy Tailed Potentials by Remco

We study the parabolic Anderson problem, that is, the heat equation ∂tu= u+ ξu on (0,∞)×Zd with independent identically distributed random potential {ξ(z) : z ∈ Zd } and localized initial condition u(0, x)= 10(x). Our interest is in the long-term behavior of the random total mass U(t) = ∑ z u(t, z) of the unique nonnegative solution in the case that the distribution of ξ(0) is heavy tailed. For...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017