This comprehensive and self-contained book addresses key issues and advanced topics in probability theory and random processes across 22 chapters. The content is organized logically, making it suitable for sequential reading or as a reference for specific topics. Encompassing both classical and contemporary results, such as large deviations theory, factorization identities, information theory, and stochastic recursive sequences, the book distinguishes itself through clear and illustrative proofs. These proofs not only establish fundamental results but also incorporate methodological enhancements to streamline arguments and enhance clarity.
Acknowledging the significant role of the Russian school in the evolution of probability theory, this work is a translation of the fifth edition of a highly successful Russian textbook. The latest edition introduces new sections, including a chapter on large deviation theory for random walks, offering theoretical and applied insights. Regular references to Russian literature contribute a unique perspective, making it an invaluable resource for Western researchers and advanced students exploring probability-related subjects.
Designed for advanced undergraduate and graduate students, this book is suitable for courses on probability theory and random processes, serving as a foundation for one-semester study or self-directed learning.
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