The fractional stochastic heat equation on the circle: Time regularity and potential theory
نویسندگان
چکیده
منابع مشابه
Sharp Gaussian regularity on the circle, and applications to the fractional stochastic heat equation
A sharp regularity theory is established for homogeneous Gaussian fields on the unit circle. Two types of characterizations for such a field to have a given almost-sure uniform modulus of continuity are established in a general setting. The first characterization relates the modulus to the field’s canonical metric; the full force of Fernique’s zero-one laws and Talagrand’s theory of majorizing ...
متن کاملSharp Gaussian regularity on the circle, and applications to the fractional stochastic heat equation
where B is a Gaussian field on [0, 1] × S1 whose behavior in time is that of fractional Brownian motion (fBm) with any parameter H ∈ (0, 1), and whose behavior in space is homogeneous, and can be completely arbitrary within that restriction. By “regularity theory” for a Gaussian field Y we mean a characterization of almostsure modulus of continuity for Y that can be written using information ab...
متن کاملStochastic Heat Equation Driven by Fractional Noise and Local Time
The aim of this paper is to study the d-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and it has the covariance of a fractional Brownian motion with Hurst parameter H ∈ (0, 1) in time. Two types of equations are considered. First we consider the equation in the Itô-Skorohod sense, and later in the Stratonovich sense. An explicit chaos developm...
متن کاملOn space-time regularity for the stochastic heat equation on Lie groups
We consider the stochastic heat equations on Lie groups, that is, equations of the form ∂tu = ∆xu + b(u) + F (u)Ẇ on R+ × G, where G is a compact Lie group, ∆ is the Laplace-Beltrami operator on G, b and F are Lipschitz coefficients, and where Ẇ is a Gaussian space-correlated noise, which is white-noise in time. We find necessary and sufficient conditions on the space correlation of Ẇ such that...
متن کاملStochastic Heat Equation with Infinite Dimensional Fractional Noise: L2-theory
In this article we consider the stochastic heat equation in [0, T ]× Rd, driven by a sequence (β)k of i.i.d. fractional Brownian motions of index H > 1/2 and random multiplication functions (g)k. The stochastic integrals are of Hitsuda-Skorohod type and the solution is interpreted in the weak sense. Using Malliavin calculus techniques, we prove the existence and uniqueness of the solution in a ...
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: Stochastic Processes and their Applications
سال: 2009
ISSN: 0304-4149
DOI: 10.1016/j.spa.2008.07.009