Asymptotic theory of weakly dependent stochastic processes
This is a revised version of lectures delivered jointly with Paul Doukhan at Orsay Faculty in the period 1994-1996. The book contains recent results, partly due to the author and his Orsay colleagues, on limit properties of sums of random variables which are either strong mixing in Rosenblatt's sense or absolutely regular in Volkonski and Rozanov's sense. The emphasis is on moments inequalities and mean deviations as tools for proving limit theorems. There are nine chapters and six appendices. Each chapter contains a number of exercises for solving, some of which are difficult enough. Contents: 1. The variance of partial sums; 2. Moments. Exponential inequalities; 3. Maximal inequalities and strong laws; 4. The central limit theorem; 5. Coupling and mixing; 6. Fuk-Nagaev inequalities, moments of arbitrary order; 7. Empirical distribution functions; 8. Empirical processes indexed by classes of functions; 9. Irreducible Markov processes; Appendix A. Young duality and Orlicz spaces; Appendix B. Exponential inequalities for independent real-valued random variables; Appendix C. Bounding weighted moments; Appendix D. A version of a lemma of Pisier; Appendix E. Elements of measure theory; Appendix F. The conditional quantile transformation; References.
scientific article; zbMATH DE number 1390912