منابع مشابه
Solving Spdes Driven by Colored Noise: a Chaos Approach
An Itô-Skorokhod bi-linear equation driven by infinitely many independent colored noises is considered in a normal triple of Hilbert spaces. The special feature of the equation is the appearance of the Wick product in the definition of the Itô-Skorokhod integral, requiring innovative approaches to computing the solution. A chaos expansion of the solution is derived and several truncations of th...
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We study reflected solutions of a nonlinear heat equation on the spatial interval [0, 1] with Dirichlet boundary conditions, driven by space-time white noise. The nonlinearity appears both in the drift and in the diffusion coefficient. Roughly speaking, at any point (t, x) where the solution u(t, x) is strictly positive it obeys the equation, and at a point (t, x) where u(t, x) is zero we add a...
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We study reflected solutions of the heat equation on the spatial interval [-0, 1] with Dirichlet boundary conditions, driven by an additive space-time white noise. Roughly speaking, at any point (x, t) where the solution u(x, t) is strictly positive it obeys the equation, and at a point (x, t) where u(x, t) is zero we add a force in order to prevent it from becoming negative. This can be viewed...
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We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itô chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordina...
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Many phenomena in nature are described by excitable systems driven by colored noise. The temporal correlations in the fluctuations hinder an analytical treatment. We here present a general method of reduction to a white-noise system, capturing the color of the noise by effective and time-dependent boundary conditions. We apply the formalism to a model of the excitability of neuronal membranes, ...
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ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 2008
ISSN: 0033-569X,1552-4485
DOI: 10.1090/s0033-569x-08-01088-2