zbMATH — the first resource for mathematics

Propriété d’absolue continuité pour les équations différentielles stochastiques dépendant du passé. (Absolute continuity property for stochastic differential equations depending on the past). (French) Zbl 0638.60068
In a previous work with N. Bouleau [ibid. 69, 229-259 (1986; Zbl 0605.60058)] the author proved a general result for absolute continuity, and used notably this result to obtain (under Lipschitz assumptions on the data) the absolute continuity with respect to the Lebesgue measure of the laws of the solutions of stochastic differential equations.
Here the same general result is still used to obtain the absolute continuity of the laws of the same projections of solutions of stochastic differential equations with coefficients depending on the past. The assumptions on the coefficients are still weak ones (Lipschitz regularity and partial ellipticity). In counterpart nothing may be proved on the regularity of the densities.
Reviewer: J.P.Lepeltier

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
Full Text: DOI
[1] Bouleau, N; Hirsch, F, Formes de Dirichlet générales et densité des variables aléatoires réelles sur l’espace de Wiener, J. funct. anal., 69, 229-259, (1986) · Zbl 0605.60058
[2] Bouleau, N; Hirsch, F, Propriétés d’absolue continuité dans LES espaces de Dirichlet et application aux équations différentielles stochastiques, () · Zbl 0642.60044
[3] Michel, D, Régularité des lois conditionnelles en théorie du filtrage non linéaire et calcul des variations stochastique, J. funct. anal., 41, 8-36, (1981) · Zbl 0487.60053
[4] Kusuoka, S; Stroock, D, Applications of the Malliavin calculus, part I, () · Zbl 0568.60059
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.