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These notes contain all the material accumulated over six years in Strasbourg to teach'Quantum Probability'to myself and to an audience of commutative probabilists. The text, a first version of which appeared in successive volumes of the Seminaire de Probabilite8, has been augmented and carefully rewritten, and translated into international English. Still, it remains true'Lecture Notes'material, and I have resisted suggestions to publish it as a monograph. Being a non-specialist, it is important for me to keep the moderate right to error one has in lectures. The origin of the text also explains the addition'for probabilists'in the title : though much of the material is accessible to the general public, I did not care to redefine Brownian motion or the Ito integral. More precisely than'Quantum Probability', the main topic is'Quantum Stochastic Calculus', a field which has recently got official recognition as 81825 in the Math.

In this volume of original research papers, the main topics discussed relate to the asymptotic windings of planar Brownian motion, structure equations, closure properties of stochastic integrals. The contents of the volume represent an important fraction of research undertaken by French probabilists and their collaborators from abroad during the academic year 1992-1993.

All the papers included in this volume are original research papers. They represent an important part of the work of French probabilists and colleagues with whom they are in close contact throughout the world. The main topics of the papers are martingale and Markov processes studies.

These proceedings contain both general expository papers and research announcements in several active areas of probability and statistics. A large range of topics is covered from theory (Sobolev inequalities and heat semigroup, Brownian motions, white noise analysis, geometrical structure of statistical experiments) to applications (simulated annealing, ARMA models).