Although there are many books available on the theory of random processes, there are few books featuring rigorous exposition that are suitable for elementary instruction. This is such a book.
Designed for students who have had a general course in probability theory, it covers general topics in the theory of random processes (including measure theory and axiomatization of probability theory) as well as more specialized questions: processes with independent increments, Markov processes and limit theorems for random processes.
A significant feature of the book is a unique and beautiful treatment of processes with independent increments, which assumes no prior knowledge of the theory of infinitely divisible laws. A wealth of results, ideas and techniques distinguish this text, one of the first to survey in a rigorous way the more modern results in the theory of stochastic processes and to link them to earlier developments in the subject. Preface to the English Translation. Introduction. Bibliographic Notes. Bibliography. Index of Symbols. Index.

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Rigorous exposition suitable for elementary instruction. Covers measure theory, axiomatization of probability theory, processes with independent increments, Markov processes and limit theorems for random processes, more. A wealth of results, ideas, and techniques distinguish this text. Introduction. Bibliography. 1969 edition.

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collection of few very good books

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