Abstract: Stochastic analysis is able classically to represent a small class of partial differential equations. We extend some stochastic objects for some class of partial differential equations when there is until now no stochastic processes. We begin by the case of a generalized Ito formula. We continue by studying the study of some generalized martingale problem when there is no probability. We continue by study a generalized Brownian sheet and study its long time behaviour involved with the Haar distribution on a path group in the Hida-Streit approach of path integral as distribution.

Brief Biography of the Speaker:
Remi Leandre works on the two faces on infinite dimensional analysis:
-The analysis of partial differential equations (Malliavin Calculus).
-The analysis of some infinite dimensional objects. He worked during a lot of time on a stochastic analysis approach to some ideas of the celebrated physicist Witten.
He belongs to the editorial board of several scientific journals. He has organized several conferences. He his editor with X. Dai, X. Ma and W. Zhang of the Festchrift published by the French Mathematical Society, in honour of the celebrated mathematician Bismut. He received in 1988 Bronze Medal of C.N.R.S. as well as Rollo Davidson Prize in 1989 for various works on hypoelliptic difuusions.