Displaying similar documents to “Convergence in Dirichlet law of certain stochastic integrals.”

Positivity of the density for the stochastic wave equation in two spatial dimensions

Mireille Chaleyat-Maurel, Marta Sanz-Solé (2003)

ESAIM: Probability and Statistics

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We consider the random vector u ( t , x ̲ ) = ( u ( t , x 1 ) , , u ( t , x d ) ) , where t > 0 , x 1 , , x d are distinct points of 2 and u denotes the stochastic process solution to a stochastic wave equation driven by a noise white in time and correlated in space. In a recent paper by Millet and Sanz–Solé [10], sufficient conditions are given ensuring existence and smoothness of density for u ( t , x ̲ ) . We study here the positivity of such density. Using techniques developped in [1] (see also [9]) based on Analysis on an abstract Wiener space, we characterize...

Weak averaging of stochastic evolution equations

Ivo Vrkoč (1995)

Mathematica Bohemica

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A theorem on continuous dependence of solutions to stochastic evolution equations on coefficients is established, covering the classical averaging procedure for stochastic parabolic equations with rapidly oscillating both the drift and the diffusion term.