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

Djehiche B., Eddahbi M., Ouknine Y.

Probability and Mathematical Statistics

2002

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.

Unicité Trajectorielle des Équations Différentielles Stochastiques Avec Temps Local

Ouknine Y.

Probability and Mathematical Statistics

1999

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.