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This volume represents a part of the main result obtained by a group of French probabilists, together with the contributions of a number of colleagues, mainly from the USA and Japan. All the papers present new results obtained during the academic year 1991-1992. The main themes of the papers are: quantum probability (P.A. Meyer and S. Attal), shastic calculus (M. Nagasawa, J.B. Walsh, F. Knight, to name a few authors), fine properties of Brownian motion (Bertoin, Burdzy, Mountford), shastic...