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Displaying similar documents to “Euler scheme for solutions of stochastic differential equations with non-Lipschitz coefficients.”

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...

Existence of solutions of perturbed O.D.E.'s in Banach spaces

Giovanni Emmanuele (1991)

Commentationes Mathematicae Universitatis Carolinae

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We consider a perturbed Cauchy problem like the following (PCP) x ' = A ( t , x ) + B ( t , x ) x ( 0 ) = x 0 and we present two results showing that (PCP) has a solution. In some cases, our theorems are more general than the previous ones obtained by other authors (see [4], [8], [9], [11], [13], [17], [18]).