Probability theory forms the basis of mathematical statistics, and has applications in many related areas. This comprehensive book tackles the principal problems and advanced questions of probability theory in 21 self-contained chapters, which are presented in logical order, but are also easy to deal with individually. The book is further distinguished by the inclusion of clear and illustrative proofs of the fundamental results.
Probability theory is currently an extremely active area of research internationally, and the importance of the Russian school in the development of the subject has long been recognized. The frequent references to Russian literature throughout this work lend a fresh dimension to the book, and make it an invaluable source of reference for Western researchers and advanced students in probability related subjects.
1. Discrete Space of Elementary Events 2. Arbitrary Space of Elementary Events 3. Random Variables and Distribution Functions 4. Numerical Characteristics of Random Variables 5. Sequences of Independent Trials with Two Outcomes 6. On Convergence of Random Variables and Distributions 6.
Characteristic Functions 7. Sequences of Independent Random Variables. Properties of the Trajectory (01, S1, S2,…) 8. Elements of Renewal Theory 9. Sequences of Independent Random Variables. Limit Theorems 10. Factorization Identities 11. Sequences of Dependent Trials. Markov Chains 12. Factorization Identities 13. Information and Entropy 14. Martingales 15. Stationary Sequences 16. Stochastically Recursive Sequences 17. Continuous Time Random Processes 18. Processes with Independent Increments 19. Functional Limit Theorems 20. Markov Processes 21. Processes with Finite Second Moments. Gaussian Processes