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The Dynkin Festschrift

Markov Processes and their Applications

  • Book
  • © 1994

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Editors:
  1. Mark I. Freidlin

    1. Department of Mathematics, University of Maryland, College Park, USA

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

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Table of contents (23 chapters)

  1. Front Matter

    Pages i-xxxii
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  2. Process Level Large Deviations for a Class of Piecewise Homogeneous Random Walks

    • V. M. Blinovskii, R. L. Dobrushin
    Pages 1-59

  3. Mutual Singularity of Genealogical Structures of Fleming-Viot and Continuous Branching Processes

    • Donald A. Dawson, Vladimir Vinogradov
    Pages 61-83

  4. Regular Conditional Expectations and the Continuum Hypothesis

    • I. V. Evstigneev
    Pages 85-93

  5. Necessary and Sufficient Conditions for Weak Convergence of One-Dimensional Markov Processes

    • Mark I. Freidlin, Alexander D. Wentzell
    Pages 95-109

  6. Inverse Subordination of Excessive Functions

    • R. K. Getoor, M. J. Sharpe
    Pages 111-131

  7. Jumping Branching Measure-Valued Processes

    • J. Jacod, A. V. Skorokhod
    Pages 133-141

  8. The Boundedness of Branching Markov Processes

    • F. I. Karpelevich, M. Ya. Kelbert, Yu. M. Suhov
    Pages 143-152

  9. A Limit Theorem for Weighted Branching Process Trees

    • Harry Kesten
    Pages 153-166

  10. Loop Condensation Effects in the Behavior of Random Walks

    • K. M. Khanin, A. E. Mazel, S. B. Shlosman, Ya. G. Sinai
    Pages 167-184

  11. On the Stability of Solutions of Stochastic Evolution Equations

    • R. Khasminskii, V. Mandrekar
    Pages 185-197

  12. Harmonic Functions on Riemannian Manifolds: A Probabilistic Approach

    • Yuri Kifer
    Pages 199-207

  13. On a Problem Suggested by A.D. Wentzell

    • N. V. Krylov, M. V. Safonov
    Pages 209-219

  14. Regularity Properties of a Supercritical Superprocess

    • S. E. Kuznetsov
    Pages 221-235

  15. A Lemma on Super-Brownian Motion with Some Applications

    • Jean-François Le Gall
    Pages 237-251

  16. Sequential Screening of Significant Variables of an Additive Model

    • Mikhail B. Maljutov, Henry P. Wynn
    Pages 253-265

  17. Brownian Bandits

    • Avi Mandelbaum, Robert J. Vanderbei
    Pages 267-285

  18. Lyapunov Exponents and Distributions of Magnetic Fields in Dynamo Models

    • Stanislav Molchanov, Alexander Ruzmaikin
    Pages 287-306

  19. The Strong Markov Property of the Support of Super-Brownian Motion

    • Edwin Perkins
    Pages 307-326

  20. Some Results on Random Walks on Groups

    • M. G. Shur
    Pages 327-332
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About this book

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.

Editors and Affiliations

  • Department of Mathematics, University of Maryland, College Park, USA

    Mark I. Freidlin

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