Bøger af Marc Yor

From the reviews: "e;This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion. The great strength of Revuz and Yor is the enormous variety of calculations carried out both in the main text and also (by implication) in the exercises. ... This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises, and throwing out challenging remarks about areas awaiting further research..."e;Bull.L.M.S. 24, 4 (1992) Since the first edition in 1991, an impressive variety of advances has been made in relation to the material of this book, and these are reflected in the successive editions.

Considering the stupendous gain in importance, in the banking and insurance industries since the early 1990¿s, of mathematical methodology, especially probabilistic methodology, it was a very natural idea for the French "Académie des Sciences" to propose a series of public lectures, accessible to an educated audience, to promote a wider understanding for some of the fundamental ideas, techniques and new tools of the financial industries.These lectures were given at the "Académie des Sciences" in Paris by internationally renowned experts in mathematical finance, and later written up for this volume which develops, in simple yet rigorous terms, some challenging topics such as risk measures, the notion of arbitrage, dynamic models involving fundamental stochastic processes like Brownian motion and Lévy processes.The Ariadne¿s thread leads the reader from Louis Bachelier¿s thesis 1900 to the famous Black-Scholes formula of 1973 and to most recent work close to Malliavin¿s stochastic calculus of variations. The book also features a description of the trainings of French financial analysts which will help them to become experts in these fast evolving mathematical techniques.

Twenty-five articles have been selected from the first 14 volumes of the "Séminaire de Probabilités", all out of print, for their historical and/or mathematical interest. Among the many articles devoted to Martingale theory in the early volumes of the Séminaire, we have chosen to reprint those that are particularly significant from a historical point of view, as well as those that can still be useful today. They are reprinted here verbatim, with a short retrospective comment, for the benefit of researchers in the theory of stochastic processes, in mathematical finance, or in history of mathematics.

The 31 papers collected here present original research results obtained in 1995-96, on Brownian motion and, more generally, diffusion processes, martingales, Wiener spaces, polymer measures.

The 39th volume of Seminaire de Probabilites is a tribute to the memory of Paul Andre Meyer. His life and achievements are recalled; homages are rendered by his friends and colleagues. This volume also contains mathematical contributions to classical and quantum stochastic calculus, the theory of processes, martingales and their applications to mathematical finance, Brownian motion. They provide an overview on the current trends of stochastic calculus.

The volume consists entirely of research papers, principally in stochastic calculus, martingales, and Brownian motion, and gathers an important part of the works done in the main probability groups in France (Paris, Strasbourg, Toulouse, Besancon, Grenoble,...) together with closely related works done by some probabilists elsewhere (Switzerland, India, Austria,...).

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.

This volume represents a part of the main result obtained bya group of French probabilists, together with thecontributions of a number of colleagues, mainly from the USAand Japan. All the papers present new results obtained during theacademic year 1991-1992. The main themes of the papers are:quantum probability (P.A. Meyer and S. Attal), stochasticcalculus (M. Nagasawa, J.B. Walsh, F. Knight, to name a fewauthors), fine properties of Brownian motion (Bertoin,Burdzy, Mountford), stochastic differential geometry(Arnaudon, Elworthy), quasi-sure analysis (Lescot, Song,Hirsch). Taken all together, the papers contained in this volumereflect the main directions of the most up-to-date researchin probability theory. FROM THE CONTENTS: J.P. Ansal, C. Stricker: Unicite etexistence de la loi minimale.- K. Kawazu, H. Tanaka: On themaximum of a diffusion process in a drifted Brownianenvironment.- P.A. Meyer: Representation de martingalesd'operateurs, d'apres Parthasarathy-Sinha.- K. Burdzy:Excursion laws and exceptional points on Brownian paths.- X. Fernique: Convergence en loi de variables aleatoires et defonctions aleatoires, proprietes de compacite des lois, II.-M. Nagasawa: Principle ofsuperposition and interference ofdiffusion processes.- F. Knight: Some remarks on mutualwindings.- S. Song: Inegalites relatives aux processusd'Ornstein-Ulhenbeck a n-parametres et capacite gaussiennec (n,2).- S. Attal, P.A. Meyer: Interpretation probabilisteet extension des integrales stochastiques non commutatives.-J. Azema, Th. Jeulin, F. Knight,M. Yor: Le theoreme d'arreten une fin d'ensemble previsible.

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.

Besides a series of six articles on Lévy processes, Volume 38 of the Séminaire de Probabilités contains contributions whose topics range from analysis of semi-groups to free probability, via martingale theory, Wiener space and Brownian motion, Gaussian processes and matrices, diffusions and their applications to PDEs.As do all previous volumes of this series, it provides an overview on the current state of the art in the research on stochastic processes.

We call peacock an integrable process which is increasing in the convex order;In this monograph, we exhibit numerous examples of peacocks and associated martingales with the help of different methods: construction of sheets, time reversal, time inversion, self-decomposability, SDE, Skorokhod embeddings.