Approximation and Support Theorem for a Wave Equation in Two Space Dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations...

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Veröffentlicht in:	Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2000-10, Vol.6 (5), p.887-915
Hauptverfasser:	Millet, Annie, Sanz-Solé, Marta
Format:	Artikel
Sprache:	eng
Schlagworte:	Anàlisi estocàstica Approximation Approximation theory approximations Cauchy Schwarz inequality Coefficients Equacions diferencials estocàstiques Integers Millet Partial differential equations Perceptron convergence procedure Stochastic analysis Stochastic differential equations stochastic partial differential equations support theorem Teoria de l'aproximació Topological theorems Trajectories Wave equations
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Beschreibung
Zusammenfassung:	We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp- norm for p ≥ 1 is also proved.
ISSN:	1350-7265
DOI:	10.2307/3318761