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Processus stochastiques pour l'ingénieur
Cet ouvrage propose une présentation didactique et homogène de la théorie des processus stochastiques, vue comme une extension de la théorie des probabilités. Il s’adresse donc tout autant aux étudiants ingénieurs qu’aux ingénieurs souhaitant s’initier à ce puissant outil de modélisation et d’analyse. Les concepts essentiels des processus stochastiques sont tout d’abord décrits, commentés et illustrés d’exemples dans le traitement du signal aléatoire. Plusieurs cas concrets de processus stochastiques (processus gaussiens ou de Poisson, chaînes de Markov) sont ensuite présentés dans différents contextes d’applications réelles (files d’attente, analyse de données médicales...). De très nombreux exercices corrigés illustrent l’ouvrage, et permettent au lecteur de se familiariser avec certains points particuliers de l’exposé
Harmonic and Stochastic Analysis of Dunkl Processes
Le livre présente un thème important, qui se développe actuellement de façon intense, de l'analyse et la théorie stochastique contemporaines: les opérateurs, les semi-groupes et les processus stochastiques de Dunkl. Les motivations et les applications de ces sujets, à l'origine en provenance de la Physique (modèles quantiques intégrables), s'étendent aujourd'hui à de vastes domaines de l'analyse harmonique et du calcul stochastique, y compris les espaces symétriques, et les processus de diffusion à valeurs dans ces espaces. Les auteurs du livre ont obtenu des résultats importants de la théorie de Dunkl. Le livre est écrit de façon accessible à des chercheurs ayant des connaissances standard en analyse harmonique et calcul stochastique.
Introduction to Stochastic Processes and Simulation
Mastering chance has, for a long time, been a preoccupation of mathematical research. Today, we possess a predictive approach to the evolution of systems based on the theory of probabilities. Even so, uncovering this subject is sometimes complex, because it necessitates a good knowledge of the underlying mathematics. This book offers an introduction to the processes linked to the fluctuations in chance and the use of numerical methods to approach solutions that are difficult to obtain through an analytical approach. It takes classic examples of inventory and queueing management, and addresses more diverse subjects such as equipment reliability, genetics, population dynamics, physics and even market finance. It is addressed to those at Masters level, at university, engineering school or management school, but also to an audience of those in continuing education, in order that they may discover the vast field of decision support.
Handbook of Brownian Motion - Facts and Formulae
Here is easy reference to a wealth of facts and formulae associated with Brownian motion, collecting in one volume more than 2500 numbered formulae. The book serves as a basic reference for researchers, graduate students, and people doing applied work with Brownian motion and diffusions, and can be used as a source of explicit examples when teaching stochastic processes.
Handbook of Brownian Motion
There are two parts in this book. The first part is devoted mainly to the proper ties of linear diffusions in general and Brownian motion in particular. The second part consists of tables of distributions of functionals of Brownian motion and re lated processes. The primary aim of this book is to give an easy reference to a large number of facts and formulae associated to Brownian motion. We have tried to do this in a "handbook-style". By this we mean that results are given without proofs but are equipped with a reference where a proof or a derivation can be found. It is our belief and experience that such a material would be very much welcome by students and people working with applications...
Stochastic Differential Equations and Diffusion Processes
Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sections discussing complex (conformal) martingales and Kahler diffusions have been added.
Diffusions, Markov Processes, and Martingales: Itô calculus
This celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first, concentrating on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. Much effort has gone into making these subjects as accessible as possible by providing many concrete examples that illustrate techniques of calculation, and by treating all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appeared for the first time in this book. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.
Stochastic Integration and Differential Equations
The idea of this book began with an invitation to give a course at the Third Chilean Winter School in Probability and Statistics, at Santiago de Chile, in July, 1984. Faced with the problem of teaching stochastic integration in only a few weeks, I realized that the work of C. Dellacherie [2] provided an outline for just such a pedagogic approach. I developed this into aseries of lectures (Protter [6]), using the work of K. Bichteler [2], E. Lenglart [3] and P. Protter [7], as well as that of Dellacherie. I then taught from these lecture notes, expanding and improving them, in courses at Purdue University, the University of Wisconsin at Madison, and the University of Rouen in France. I take t...
