2 473 kr
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3 024 kr
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2 448 kr
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2 105 kr
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668 kr
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651 kr
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492 kr
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Nouvelle édition entièrement revue et augmentée. Cet ouvrage a pour origine le cours de processus aléatoires de la maîtrise de mathématiques de l''Université Pierre-et-Marie-Curie (Paris VI) que les auteurs ont dispensé pendant plusieurs années. L''objectif est d''initier le lecteur à la théorie des martingales et des chaînes de Markov par la pratique d''exercices. Chaque chapitre commence par un exposé concis mais complet des principaux résultats, avec l''essentiel des démonstrations. Tous les exercices et les problèmes (une centaine au total) sont corrigés de façon détaillée. Les problèmes apportent des compléments permettant au lecteur d''approfondir ses connaissances et d''aborder d''autres développements et applications. Tout en ouvrant une porte vers les troisièmes cycles spécialisés, cet ouvrage est principalement destiné aux étudiants de deuxième cycle et aux candidats de l''agrégation.
773 kr
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This textbook offers a complete one-semester course in probability, covering the essential topics necessary for further study in the areas of probability and statistics.
The book begins with a review of the fundamentals of measure theory and integration. Probability measures, random variables, and their laws are introduced next, along with the main analytic tools for their investigation, accompanied by some applications to statistics. Questions of convergence lead to classical results such as the law of large numbers and the central limit theorem with their applications also to statistical analysis and more. Conditioning is the next main topic, followed by a thorough introduction to discrete time martingales. Some attention is given to computer simulation. Through the text, over 150 exercises with full solutions not only reinforce the concepts presented, but also provide students with opportunities to develop their problem-solving skills, and make this textbook suitable forguided self-study.
Based on years of teaching experience, the author''s expertise will be evident in the clear presentation of material and the carefully chosen exercises. Assuming familiarity with measure and integration theory as well as elementary notions of probability, the book is specifically designed for teaching in parallel with a first course in measure theory. An invaluable resource for both instructors and students alike, it offers ideal preparation for further courses in statistics or probability, such as stochastic calculus, as covered in the author''s book on the topic.
995 kr
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1 268 kr
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This book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. It is the only textbook on the subject to include more than two hundred exercises with complete solutions.
After explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used.
Stochastic Calculus will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. Including full mathematical statements and rigorous proofs, this book is completely self-contained and suitable for lecture courses as well as self-study.
