Veroi͡atnostʹ

About “Veroi͡atnostʹ”

This book offers a systematic introduction to probability, beginning with basic concepts and moving toward advanced topics such as random walks, martingales, Markov chains, and the Kalman-Bucy filter. It includes detailed examples and numerous exercises, making it suitable for advanced undergraduates or self-study. The text is designed to build understanding gradually, covering both foundational and more complex areas of probability theory. The second edition includes substantial revisions and updated references. It provides a deeper exploration of topics like the distance between probability measures, metrization of weak convergence, and contiguity of probability measures. Additional proofs have been included for important results previously stated without them. New content covers large deviation probabilities, the central limit theorem for dependent variables, and a discrete version of Ito's formula. The book is authored by A. N. Shiryayev and translated into English.