Martingale Approximation

ISBN-13: 9789067642712 / Angielski / Twarda / 1997 / 333 str.

Iu V. Borovskikh; Yu V. Borovskikh; V. S. Korolyuk

Opis

Limit theorems for semimartingales form the basis of the martingale approximation approach. The methods of martingale approximation addressed in this book pertain to estimates of the rate of convergence in the central limit theorem and in the invariance principle. Some applications of martingale approximation are illustrated by the analysis of U-statistics, rank statistics, statistics of exchangeable variables and stochastic exponential statistics. Simplified results of stochastic analysis are given for use in investigations of many applied problems, including mathematical statistics, financial mathematics, mathematical biology, industrial mathematics and engineering.

Spis treści

Frontmatter -- Contents -- Preface -- 1. Basic notions -- 2. Semimartingales -- 3. Inequalities -- 4. Laws of large numbers -- 5. Central limit theorem -- 6. Convergence of semimartingales -- 7. Rate of weak convergence -- 8. Applications of martingales -- Appendix -- Bibliographic notes -- Bibliography -- Subject index