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 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...
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...
متن کاملOn Convergence of Population Processes in Random Environments to the Stochastic Heat Equation with Colored Noise
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 کاملQuadratic variations for the fractional-colored stochastic heat equation∗
Using multiple stochastic integrals and Malliavin calculus, we analyze the quadratic variations of a class of Gaussian processes that contains the linear stochastic heat equation on R driven by a non-white noise which is fractional Gaussian with respect to the time variable (Hurst parameter H) and has colored spatial covariance of α-Riesz-kernel type. The processes in this class are self-simila...
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ژورنال
عنوان ژورنال: Stochastics and Partial Differential Equations: Analysis and Computations
سال: 2019
ISSN: 2194-0401,2194-041X
DOI: 10.1007/s40072-019-00149-3