Malliavin calculus for two-parameter processes
D. Nualart, M. Sanz (1985)
Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications
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D. Nualart, M. Sanz (1985)
Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications
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John C. Taylor (1992)
Séminaire de probabilités de Strasbourg
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Samy Tindel (2000)
Applicationes Mathematicae
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We consider the equation du(t,x)=Lu(t,x)+b(u(t,x))dtdx+σ(u(t,x))dW(t,x) where t belongs to a real interval [0,T], x belongs to an open (not necessarily bounded) domain , and L is a pseudodifferential operator. We show that under sufficient smoothness and nondegeneracy conditions on L, the law of the solution u(t,x) at a fixed point is absolutely continuous with respect to the Lebesgue measure.
Antoine Lejay (2006)
ESAIM: Probability and Statistics
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We show in this article how the theory of “rough paths” allows us to construct solutions of differential equations (SDEs) driven by processes generated by divergence-form operators. For that, we use approximations of the trajectories of the stochastic process by piecewise smooth paths. A result of type Wong-Zakai follows immediately.
Rémi Léandre (2002-2003)
Séminaire Équations aux dérivées partielles
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Mireille Chaleyat-Maurel, David Nualart (1995)
Séminaire de probabilités de Strasbourg
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