Displaying similar documents to “On the difference between the product and the convolution product of distribution functions.”

Averaging method for differential equations perturbed by dynamical systems

Françoise Pène (2002)

ESAIM: Probability and Statistics

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In this paper, we are interested in the asymptotical behavior of the error between the solution of a differential equation perturbed by a flow (or by a transformation) and the solution of the associated averaged differential equation. The main part of this redaction is devoted to the ascertainment of results of convergence in distribution analogous to those obtained in [10] and [11]. As in [11], we shall use a representation by a suspension flow over a dynamical system. Here, we make...

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...

Asymptotic behaviour of stochastic quasi dissipative systems

Giuseppe Da Prato (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.