منابع مشابه
Stochastic Heat Equation with Multiplicative Fractional-Colored Noise
We consider the stochastic heat equation with multiplicative noise ut = 1 2 ∆u + uẆ in R+ × R , whose solution is interpreted in the mild sense. The noise Ẇ is fractional in time (with Hurst index H ≥ 1/2), and colored in space (with spatial covariance kernel f). When H > 1/2, the equation generalizes the Itô-sense equation for H = 1/2. We prove that if f is the Riesz kernel of order α, or the ...
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 کاملThe Stochastic Heat Equation with a Fractional-colored Noise: Existence of the Solution
Abstract. In this article we consider the stochastic heat equation ut −∆u = Ḃ in (0, T )× R, with vanishing initial conditions, driven by a Gaussian noise Ḃ which is fractional in time, with Hurst index H ∈ (1/2, 1), and colored in space, with spatial covariance given by a function f . Our main result gives the necessary and sufficient condition on H for the existence of the process solution. W...
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We consider the stochastic heat equation with a multiplicative colored noise term on Rd for d ≥ 1. First, we prove convergence of a branching particle system in a random environment to this stochastic heat equation with linear noise coefficients. For this stochastic partial differential equation with more general non-Lipschitz noise coefficients we show convergence of associated lattice systems...
متن کاملThe Stochastic Heat Equation with Fractional-Colored Noise: Existence of the Solution
Abstract. In this article we consider the stochastic heat equation ut −∆u = Ḃ in (0, T )×Rd, with vanishing initial conditions, driven by a Gaussian noise Ḃ which is fractional in time, with Hurst index H ∈ (1/2, 1), and colored in space, with spatial covariance given by a function f . Our main result gives the necessary and sufficient condition on H for the existence of a solution. When f is t...
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ژورنال
عنوان ژورنال: Ukrains’kyi Matematychnyi Zhurnal
سال: 2020
ISSN: 1027-3190
DOI: 10.37863/umzh.v72i9.6282