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Zbl 0688.60043
Lépingle, Dominique; Nualart, David; Sanz, Marta
Dérivation stochastique de diffusions réfléchies. (Stochastic derivatives of diffusions with reflections). (French)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 25, No.3, 283-305 (1989). ISSN 0246-0203

In the past years, a differential calculus on Wiener space has been developed by various authors, motivated in particular by the Malliavin calculus, and has become an important part of Stochastic Analysis. However, except for solutions of stochastic differential equations, derivatives of Wiener functionals have been computed only in a few examples. \par The authors of the paper under review compute the derivative of the solution of a stochastic differential equation with reflection. They then apply their result to obtain a sufficient condition for the law of the solution at time t to be absolutely continuous with respect to Lebesgue measure.
[E.Pardoux]

MSC 2000:: *60H10 Stochastic ordinary differential equations
60H07 Stochastic calculus of variations and the Malliavin calculus

Keywords: Malliavin calculus; derivatives of Wiener functionals; stochastic differential equation with reflection

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