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Unicité Trajectorielle des Équations Différentielles Stochastiques Avec Temps Local

100%

Ouknine Y.

Probability and Mathematical Statistics

1999

tom Vol. 19, Fasc. 1

55--62

We study the pathwise uniqueness of a one-dimensional stochastic differential equation driven by white noise and involving local time of the unknown process. We introduce a very weak condition on the diffusion term which is sufficient for the pathwise uniqueness if one considers an equation of the form [formula] where v stands for a signed Radon measure on R.

A logarithmic Sobolev inequality for one-dimensional multivalued stochastic differential equations

51%

Djehiche B. , Eddahbi M. , Ouknine Y.

Probability and Mathematical Statistics

2002

tom Vol. 22, Fasc. 1

13--18

We establish a logarithmic Sobolev inequality for a one-dimensional multivalued stochastic differential equation associated with the subdifferential of a convexlower semicontinuous function, using an explicit expression for the Malliavin derivative of the considered process. This result is given under some mild conditions on thecoefficients.