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Who could have predicted that the S´ eminaire de Probabilit´ es would reach the age of 40? This long life is ?rst due to the vitality of the French probabil- tic school, for which the S´ eminaire remains one of the most speci?c media of exchange. Another factor is the amount of enthusiasm, energy and time invested year after year by the R´ edacteurs: Michel Ledoux dedicated himself tothistaskuptoVolumeXXXVIII,andMarcYormadehisnameinseparable from the S´ eminaire by devoting himself to it during a quarter of a century. Browsing among the past volumes can only give a faint glimpse of how much is owed to them; keeping up with the standard they have set is a challenge to the new R´ edaction. In a changing world where the status of paper and ink is questioned and where, alas, pressure for publishing is increasing, in particular among young mathematicians, we shall try and keep the same direction. Although most contributions are anonymously refereed, the S´ eminaire is not a mathema- cal journal; our ?rst criterion is not mathematical depth, but usefulness to the French and international probabilistic community. We do not insist that everything published in these volumes should have reached its ?nal form or be original, and acceptance-rejection may not be decided on purely scienti?c grounds.

Séminaire de Probabilités XL

Preface.- Specialized Course. Laure Coutin: An introduction to (stochastic) calculus with respect to fractional Brownian motion.- Local Time-Space Calculus. G. Peskir: A change-of-variable formula with local time on surfaces.- A. E. Kyprianou, B.A. Surya: A note on a change of variable formula with local time-space for Lévy processes of bounded variation.- J. Najnudel: Integration with respect to local time and selfintersection of local time of a one-dimensional Brownian motion.- D. Elworthy, A. Truman, H. Zhao: Generalized Itô formulae and space-time Lebesgue-Stieltjes integrals of local time.- N. Eisenbaum: Local time-space calculus for reversible semimartingales.- F. Russo, P. Vallois: Elements of stochastic calculus via regularisation.- H. Pham: On the smooth-fit property for one-dimensional optimal switching problem.- Other contributions. I. Crimaldi, G. Letta, L. Pratelli: A strong form of stable convergence.- P. J. Catuogno, P. R. C. Ruffino: Product of harmonic maps is harmonic: a stochastic approach.- M. Ledoux: More Hypercontractive Bounds for Deformed Orthogonal Polynomial Ensembles.- E. Cépa, D. Lépingle: No multiple collisions for mutually repelling Brownian particles.- L. Alili, P. Patie: On the joint law of the L1 and L2 norms of a 3-dimensional Bessel bridge.- P. Salminen, M. Yor: Tanaka formula for symmetric Lévy processes.- M. Pistorius: An excursion theoretical approach to some boundary crossing problems and the Skorokhod embedding for reflected Lévy processes.- J. Oblój: The maximality principle revisited: on certain optimal stopping problems.- N. Enriquez: Correlated processes and the composition of generators.- L. Serlet: Representation of the martingales for the Brownian snake.- E. Gobet, S.Menozzi: Discretesampling of functionals of Itô processes.- O. Chybriakov: Itô's integrated formula for strict local martingales with jumps.- S. Ankirchner, S. Dereich, P. Imkeller: Enlargement of filtrations and continuous Girsanov-type embeddings.- M. De Donno, M. Pratelli: On a lemma by Ansel and Stricker.- A.S. Cherny: General arbitrage pricing model: I.Probability approach.- II.Transaction costs.- III.Possibility approach.