Marc Yor left us on January 9, 2014, at the age of 64.
Marc Yor received his Thèse d'état at Université Pierre et Marie Curie (Paris VI) in 1976, where he became a CNRS researcher the same year, and where he was appointed Professor in 1981.
Marc Yor was also a member of the French Academy of Sciences, and a member of the Institut universitaire de France.
Most people have known of Marc Yor through his book coauthored with Daniel Revuz, "Continuous Martingales and Brownian Motion". Their research monograph is treasured by both beginners and advanced researchers. Since its first publication in 1991, it has met an extraordinary success, reaching the third printing of the third edition in 2005. In the book, beginners find an excellent companion in the form of an important number of exercises ranging from elementary to highly challenging levels, whereas researchers appreciate particularly the authoritative account of the theory of continuous stochastic calculus, covering a large variety of applications.
Marc Yor was among those whose contribution to Probability Theory has made it among the most active branches of mathematics, as witnessed by a first Fields Medal in Probability Theory received by Wendelin Werner, a grand-student of Marc.
Marc Yor had over thirty students, many of whom became eminent mathematicians, such as Jean Bertoin, Philippe Biane(*) and Jean-François Le Gall, each of whom has had many students and grand-students.
Marc Yor's early research breakthroughs came in martingale theory and stochastic calculus. His works on BMO and martingale inequalities, on local times of semimartingales, on the Skorokhod embedding, and on enlargement of filtrations were among the most significant. Itô's stochastic calculus was much developed by Paul-André Meyer's Strasbourg School; Marc showed how powerful this theory can be.
Starting from the 1980s, Marc Yor devoted an important part of his research interest on the concrete and fundamental example of Brownian motion. A highlight of his activities in this period was a fruitful collaboration with Jim Pitman that led to remarkable work on functionals of planar Brownian motion, and on various distributional identities and path decompositions for Brownian motion and Bessel processes. At the same time, Marc made important contributions to the study of local times and additive functionals and principal values, of intersection local times, of quadratic functionals, of weak and strong Brownian filtrations. His latest work also involved penalisations of Brownian motion and Lévy processes, as well as "peacock processes".
Like Paul Lévy before him, Marc Yor considered that every non-trivial problem concerning Brownian motion should be dealt with and should be solved, and that its solution would tell us something interesting about Brownian motion. Naturally, when certain problems originating from financial mathematics concerning exponential functionals of Brownian motion were brought to his attention, Marc immediately got interested. These problems led him to subsequently focus attention on exponential functionals of Lévy processes, and to other problems involving Brownian motion that appear naturally in financial mathematics.
If a single word were to characterise Marc Yor as a mathematician, we would say that he was a missionary. His mission was to communicate his passion for mathematics to everyone he encountered. Whoever knew Marc could hardly have missed to notice Marc's generosity towards others (especially students and young researchers), as well as his extreme modesty; these undoubtably are characteristics of a devoted missionary. We will probably never know the origin of his sense of mission, but it is not too risky to guess that Paul Lévy might have been for something in it. Marc held great admiration for Lévy; he carefully kept at home some manuscripts of Lévy, showing them only occasionally to visitors.
In 2000, the French Academy of Sciences opened a pli cacheté of Wolfgang Doeblin. Together with Bernard Bru, Marc Yor spent tremendous efforts to make Doeblin's work known to a large public. It was a good example of Marc's generosity towards others. As for his modesty, simply ask people in the small town of Saint-Chéron where he spent his last twenty-nine years. In the town, he was known as the former coach of the local football team, as a regular jogger, or as Carmel's husband and father of Serge, Kathleen and Géraldine, but people would have been surprised to learn that Marc was an illustrious academician whose name was printed in the dictionary.
Marc Yor has fulfilled his mathematical mission. He did not leave us. A grain having fallen into a field never disappears — it simply brings out more.
The text above, which has appeared in the May issue (Vol 21 No 1) of Bernoulli News, is reproduced here by kind permission of the Bernoulli Society.