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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.
Brownian motion processes --- Martingales (Mathematics) --- Mathematical Theory --- Mathematical Statistics --- Mathematics --- Physical Sciences & Mathematics --- Brownian motion processes. --- Wiener processes --- Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Math --- Science --- Stochastic processes --- Brownian movements --- Fluctuations (Physics) --- Markov processes --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities
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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.
519.21 --- Brownian motion processes --- Martingales (Mathematics) --- Stochastic processes --- Wiener processes --- Brownian movements --- Fluctuations (Physics) --- Markov processes --- Probability theory. Stochastic processes --- Brownian motion processes. --- Martingales (Mathematics). --- 519.21 Probability theory. Stochastic processes --- Brownse beweging [Proces van de ] --- Martingalen (Wiskunde) --- Mouvement brownien [Processus du ] --- Statistical physics --- Mouvement brownien, Processus de --- Martingales (Mathématiques) --- Probabilities. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Processus stochastiques --- Probabilités. --- Probabilities --- Stochastic processes. --- Probabilités --- Analyse stochastique --- Mouvement brownien --- Martingales --- Integrales stochastiques
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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.
Probabilities --- Probabilités --- Problems, exercises, etc. --- Problèmes et exercices --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk
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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.
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Operational research. Game theory --- stochastische analyse --- kansrekening
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Quantitative methods (economics) --- Operational research. Game theory --- Mathematics --- Mathematical physics --- Financial analysis --- stochastische analyse --- geschiedenis --- financiële analyse --- wiskunde --- fysica --- kansrekening
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Operational research. Game theory --- stochastische analyse --- kansrekening