Probability: In 2 books. Book 2

This publication (in two books “Probability of –– 1” and “Probability of –– 2”) is an extended course of lectures on probability theory. The second book “probability –– 2” is devoted to random processes with discrete time (random sequences) The main attention here is paid to stationary sequences (in a narrow and broad sense), Martingals and Markov chains. Applications are given to issues of evaluating and filtering in random sequences, to stochastic financial mathematics, insurance theory and tasks of optimal stop. A sketch of the history of probability theory is also given. The historical and bibliographic certificate indicates the sources of the results given, comments are given and additional literature is indicated. At the end of each paragraph, tasks are given. The first book “Probability –– 1” contains material related to the elementary theory of probabilities, mathematical foundations and limit theorems. Books are designed for students of physical and mathematical specialties of universities. They can serve as a training manual for graduate students and a reference manual for specialists. Table. 9. Il. 42. Bibliogr. 138 names. The previous edition was published in 2017