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Book
Penalising Brownian Paths
Authors: ---
ISBN: 3540896988 3540896996 Year: 2009 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,

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Abstract

Penalising a process is to modify its distribution with a limiting procedure, thus defining a new process whose properties differ somewhat from those of the original one. We are presenting a number of examples of such penalisations in the Brownian and Bessel processes framework. The Martingale theory plays a crucial role. A general principle for penalisation emerges from these examples. In particular, it is shown in the Brownian framework that a positive sigma-finite measure takes a large class of penalisations into account.

Continuous martingales and Brownian motion
Authors: ---
ISBN: 3540643257 0387576223 3540576223 9783540643258 3642084001 3662064006 9783642084003 Year: 1999 Volume: 293 Publisher: Berlin Heidelberg New York : Springer,

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From the reviews: "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..." 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.


Book
Continuous martingales and brownian motion
Authors: ---
ISBN: 0387521674 3540521674 3662217287 3662217260 9783540521679 9780387521671 Year: 1991 Volume: 293 Publisher: Berlin Heidelberg Paris Springer-Verlag


Book
Exercises in probability : a guided tour from measure theory to random processes, via conditioning
Authors: ---
ISBN: 9781107606555 9781139526562 1139526561 9781139135351 113913535X 9781283528511 1283528517 9781139531238 1139531239 1107606551 1107232309 9781107232303 1139528955 9781139528955 1139532421 9781139532426 1139527762 9781139527767 9786613840967 6613840963 Year: 2012 Publisher: Cambridge : Cambridge University Press,

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Derived from extensive teaching experience in Paris, this second edition now includes over 100 exercises in probability. New exercises have been added to reflect important areas of current research in probability theory, including infinite divisibility of stochastic processes, past-future martingales and fluctuation theory. For each exercise the authors provide detailed solutions as well as references for preliminary and further reading. There are also many insightful notes to motivate the student and set the exercises in context. Students will find these exercises extremely useful for easing the transition between simple and complex probabilistic frameworks. Indeed, many of the exercises here will lead the student on to frontier research topics in probability. Along the way, attention is drawn to a number of traps into which students of probability often fall. This book is ideal for independent study or as the companion to a course in advanced probability theory.


Book
Exercises in probability : a guided tour from measure theory to random processes, via conditioning
Authors: ---
ISBN: 0511837801 0511610815 Year: 2003 Publisher: Cambridge : Cambridge University Press,

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This book was first published in 2003. Derived from extensive teaching experience in Paris, this book presents around 100 exercises in probability. The exercises cover measure theory and probability, independence and conditioning, Gaussian variables, distributional computations, convergence of random variables, and random processes. For each exercise the authors have provided detailed solutions as well as references for preliminary and further reading. There are also many insightful notes to motivate the student and set the exercises in context. Students will find these exercises extremely useful for easing the transition between simple and complex probabilistic frameworks. Indeed, many of the exercises here will lead the student on to frontier research topics in probability. Along the way, attention is drawn to a number of traps into which students of probability often fall. This book is ideal for independent study or as the companion to a course in advanced probability theory.

Séminaire de probabilités 1967-1980 : a selection in martingale theory
Authors: ---
ISBN: 3540428135 Year: 2002 Publisher: Berlin Springer-Verlag

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Book
Penalising Brownian paths
Authors: ---
ISBN: 9783540896982 Year: 2009 Publisher: Berlin Springer-Verlag

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Digital
Random Times and Enlargements of Filtrations in a Brownian Setting
Authors: ---
ISBN: 9783540324164 Year: 2006 Publisher: Berlin, Heidelberg Springer-Verlag Berlin/Heidelberg

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Digital
In Memoriam Paul-André Meyer : Séminaire de Probabilités XXXIX
Authors: ---
ISBN: 9783540355137 Year: 2006 Publisher: Berlin, Heidelberg Springer

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Digital
Aspects of Brownian motion
Authors: ---
ISBN: 9783540499664 Year: 2008 Publisher: Berlin, Heidelberg Springer-Verlag Berlin Heidelberg

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