Overview

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.

Full Product Details

Author:   Mark I. Freidlin
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1994
Volume:   34
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   0.688kg
ISBN:  

9781461266914

ISBN 10:   1461266912
Pages:   416
Publication Date:   21 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Process Level Large Deviations for a Class of Piecewise Homogeneous Random Walks.- Mutual Singularity of Genealogical Structures of Fleming-Viot and Continuous Branching Processes.- Regular Conditional Expectations and the Continuum Hypothesis.- Necessary and Sufficient Conditions for Weak Convergence of One-Dimensional Markov Processes.- Inverse Subordination of Excessive Functions.- Jumping Branching Measure-Valued Processes.- The Boundedness of Branching Markov Processes.- A Limit Theorem for Weighted Branching Process Trees.- Loop Condensation Effects in the Behavior of Random Walks.- On the Stability of Solutions of Stochastic Evolution Equations.- Harmonic Functions on Riemannian Manifolds: A Probabilistic Approach.- On a Problem Suggested by A.D. Wentzell.- Regularity Properties of a Supercritical Superprocess.- A Lemma on Super-Brownian Motion with Some Applications.- Sequential Screening of Significant Variables of an Additive Model.- Brownian Bandits.- Lyapunov Exponents and Distributions of Magnetic Fields in Dynamo Models.- The Strong Markov Property of the Support of Super-Brownian Motion.- Some Results on Random Walks on Groups.- Diffusions as Integral Curves, or Stratonovich without Itô.- Convex Solutions to Variational Inequalities and Multidimensional Singular Control.- Regularity of Self-Diffusion Coefficient.- Representation Results for Stopping Times in Jump-with-Drift Processes.

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