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The Dynkin Festschrift

Markov Processes and their Applications

  • Mark I. Freidlin

Part of the Progress in Probability book series (PRPR, volume 34)

Table of contents

  1. Front Matter
    Pages i-xxxii
  2. R. K. Getoor, M. J. Sharpe
    Pages 111-131
  3. J. Jacod, A. V. Skorokhod
    Pages 133-141
  4. F. I. Karpelevich, M. Ya. Kelbert, Yu. M. Suhov
    Pages 143-152
  5. K. M. Khanin, A. E. Mazel, S. B. Shlosman, Ya. G. Sinai
    Pages 167-184
  6. R. Khasminskii, V. Mandrekar
    Pages 185-197
  7. N. V. Krylov, M. V. Safonov
    Pages 209-219
  8. Jean-François Le Gall
    Pages 237-251
  9. Mikhail B. Maljutov, Henry P. Wynn
    Pages 253-265
  10. Avi Mandelbaum, Robert J. Vanderbei
    Pages 267-285
  11. Stanislav Molchanov, Alexander Ruzmaikin
    Pages 287-306
  12. M. G. Shur
    Pages 327-332
  13. D. Stroock, S. Taniguchi
    Pages 333-369
  14. S. R. S. Varadhan
    Pages 387-397
  15. Back Matter
    Pages 415-416

About this book

Introduction

Onishchik, A. A. Kirillov, and E. B. Vinberg, who obtained their first results on Lie groups in Dynkin's seminar. At a later stage, the work of the seminar was greatly enriched by the active participation of 1. 1. Pyatetskii­ Shapiro. As already noted, Dynkin started to work in probability as far back as his undergraduate studies. In fact, his first published paper deals with a problem arising in Markov chain theory. The most significant among his earliest probabilistic results concern sufficient statistics. In [15] and [17], Dynkin described all families of one-dimensional probability distributions admitting non-trivial sufficient statistics. These papers have considerably influenced the subsequent research in this field. But Dynkin's most famous results in probability concern the theory of Markov processes. Following Kolmogorov, Feller, Doob and Ito, Dynkin opened a new chapter in the theory of Markov processes. He created the fundamental concept of a Markov process as a family of measures corresponding to var­ ious initial times and states and he defined time homogeneous processes in terms of the shift operators ()t. In a joint paper with his student A.

Keywords

Markov Markov chain Markov process Probability distribution operator statistics

Editors and affiliations

  • Mark I. Freidlin
    • 1
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA

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