This book is axiomatic and abstract, and presents a comprehensive but pure-math approach to probability theory. The author belongs to the Kolmogorov school and follows their axiomatic approach. This is an English translation of the fourth Russian edition and is the first of two volumes. The second volume was projected to be published in but has not appeared or been announced yet. The present book comprises the first three chapters of the Russian edition.
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Account Options Connexion. This textbook is based on a three-semester course of lectures given by the author in recent years in the Mechanics-Mathematics Faculty of Moscow State University and issued, in part, in mimeographed form under the title Probability, Statistics, Stochastic Processes, I, II by the Moscow State University Press.
We follow tradition by devoting the first part of the course roughly one semester to the elementary theory of probability Chapter I. This begins with the construction of probabilistic models with finitely many outcomes and introduces such fundamental probabilistic concepts as sample spaces, events, probability, independence, random variables, expectation, corre lation, conditional probabilities, and so on.
Many probabilistic and statistical regularities are effectively illustrated even by the simplest random walk generated by Bernoulli trials. In this connection we study both classical results law of large numbers, local and integral De Moivre and Laplace theorems and more modern results for example, the arc sine law. The first chapter concludes with a discussion of dependent random vari ables generated by martingales and by Markov chains.
Page 9. Page 8. Page Convergence of Probability Measures Central Limit. Historical and Bibliographical Notes. Index of Symbols. Droits d'auteur. Informations bibliographiques. Probability A.
He is known for his work in probability theory, statistics and financial mathematics. He graduated from Moscow State University in From that time until now he has been working in Steklov Mathematical Institute. He earned his candidate degree in Andrey Kolmogorov was his advisor and a doctoral degree in for his work "On statistical sequential analysis". He is a professor of the department of mechanics and mathematics of Moscow State University, since
Probability theory, mathematical statistics. Main interest: nonlinear spectral theory of stationary processes, quickest detection problems, statistical sequential analysis, nonlinear filtration, stochastic calculus of random processes, theory of martingales, functional limit theorems for semimartingales, mathematical finance. Thesis "Optimal methods in quickest detection problems". Thesis: "Investigations in statistical sequential analysis". Member of Moscow Mathematical Society. Degree of Honorary researcher of Russian Federation. Pupils: 68 candidate dissertations, 30 doctors dissertations.