Mathematics > Probability
[Submitted on 22 Jan 2014 (v1), last revised 30 Oct 2017 (this version, v3)]
Title:Random-field Solutions to Linear Hyperbolic Stochastic Partial Differential Equations with Variable Coefficients
View PDFAbstract:In this article we show the existence of a random-field solution to linear stochastic partial differential equations whose partial differential operator is hyperbolic and has variable coefficients that may depend on the temporal and spatial argument. The main tools for this, pseudo-differential and Fourier integral operators, come from microlocal analysis. The equations that we treat are second-order and higher-order strictly hyperbolic, and second-order weakly hyperbolic with uniformly bounded coefficients in space. For the latter one we show that a stronger assumption on the correlation measure of the random noise might be needed. Moreover, we show that the well-known case of the stochastic wave equation can be embedded into the theory presented in this article.
Submission history
From: Alessia Ascanelli [view email][v1] Wed, 22 Jan 2014 20:44:51 UTC (39 KB)
[v2] Mon, 17 Nov 2014 16:32:15 UTC (37 KB)
[v3] Mon, 30 Oct 2017 09:03:51 UTC (36 KB)
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