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Fractional derivatives of local times of stable Lévy processes as the limits of the occupation time problem in Besov space

Ouhara M. A., Eddahbi M., Ouali M.

Probability and Mathematical Statistics

2004

Vol. 24, Fasc. 2

263--279

In this paper, we firstly study the Besov regularity of the local time of symmetric stable processes and of its fractional derivative. Secondly, we establish limit theorems for occupation times of α-symmetric stable processes with 1 < α ≤ 2 in some Besov spaces. Finally, we give the strong approximation version of our limit theorems.

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.