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The 37th SA(c)minaire de ProbabilitA(c)s contains A. Lejay's
advanced course which is a pedagogical introduction to works by T.
Lyons and others on stochastic integrals and SDEs driven by
deterministic rough paths. The rest of the volume consists of
various articles on topics familiar to regular readers of the
SA(c)minaires, including Brownian motion, random environment or
scenery, PDEs and SDEs, random matrices and financial random
processes.
The 36th Séminaire de Probabilités contains an advanced course on Logarithmic Sobolev Inequalities by A. Guionnet and B. Zegarlinski, as well as two shorter surveys by L. Pastur and N. O'Connell on the theory of random matrices and their links with stochastic processes. The main themes of the other contributions are Logarithmic Sobolev Inequalities, Stochastic Calculus, Martingale Theory and Filtrations. Besides the traditional readership of the Séminaires, this volume will be useful to researchers in statistical mechanics and mathematical finance.
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 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, Besan on, Grenoble, ...)
together with closely related works done by some probabilists
elsewhere (Switzerland, India, Austria, ...)
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.
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 contained in the volume are original, fully refereed
researchpapers. They represent a fairly broad spectrum of the
research activity in probability theory, which was done
internationally in 1990-1991, with particular emphasis on Markov
processes and stochastic calculus. The latter subject keeps
growing, and some important new developments, included in the
volume, concern anticipative stochastic integrals, and new
applications of the enlargements of filtrations to the study of
zeros of martingales. FROM THE CONTENTS: R. Bass, D. Khoshnevisan:
Stochastic calculus and the continuity of local times of Levy
processes.- M.T. Barlow, P. Imkeller: On some sample path
properties of Skorokhod integral processes.- T.S. Mountford: A
critical function for the planar Brownian convex hull.- L. Dubins,
M. Smorodinsky: The modified, discrete Levy transformation is
Bernoulli.- M. Baxter: Markov processes on the boundary of the
binary tree.- R. Abraham: Unarbre aleatoire infini associe a
l'excursion brownienne.- S.E. Kuznetsov: On the existence of a dual
semigroup.
All the papers in the volume are original research papers,
discussing fundamental properties of stochastic processes. The
topics under study (martingales, filtrations, path properties,
etc.) represent an important part of the current research performed
in 1996-97 by various groups of probabilists in France and abroad.
The different papers contained in this volume are all research
papers. The main directions of research which are being developed
are: quantum probability, semimartingales and stochastic calculus.
Besides a number of papers on classical areas of research in
probability such as martingale theory, Malliavin calculus and
2-parameter processes, this new volume of the S minaire de
Probabilit?'s develops the following themes: - chaos representation
for some new kinds of martingales, - quantum probability, -
branching aspects on Brownian excursions, - Brownian motion on a
set of rays.
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