Ebook: The Dynkin Festschrift: Markov Processes and their Applications

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.

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Content:
Front Matter....Pages i-xxxii
Process Level Large Deviations for a Class of Piecewise Homogeneous Random Walks....Pages 1-59
Mutual Singularity of Genealogical Structures of Fleming-Viot and Continuous Branching Processes....Pages 61-83
Regular Conditional Expectations and the Continuum Hypothesis....Pages 85-93
Necessary and Sufficient Conditions for Weak Convergence of One-Dimensional Markov Processes....Pages 95-109
Inverse Subordination of Excessive Functions....Pages 111-131
Jumping Branching Measure-Valued Processes....Pages 133-141
The Boundedness of Branching Markov Processes....Pages 143-152
A Limit Theorem for Weighted Branching Process Trees....Pages 153-166
Loop Condensation Effects in the Behavior of Random Walks....Pages 167-184
On the Stability of Solutions of Stochastic Evolution Equations....Pages 185-197
Harmonic Functions on Riemannian Manifolds: A Probabilistic Approach....Pages 199-207
On a Problem Suggested by A.D. Wentzell....Pages 209-219
Regularity Properties of a Supercritical Superprocess....Pages 221-235
A Lemma on Super-Brownian Motion with Some Applications....Pages 237-251
Sequential Screening of Significant Variables of an Additive Model....Pages 253-265
Brownian Bandits....Pages 267-285
Lyapunov Exponents and Distributions of Magnetic Fields in Dynamo Models....Pages 287-306
The Strong Markov Property of the Support of Super-Brownian Motion....Pages 307-326
Some Results on Random Walks on Groups....Pages 327-332
Diffusions as Integral Curves, or Stratonovich without It?....Pages 333-369
Convex Solutions to Variational Inequalities and Multidimensional Singular Control....Pages 371-386
Regularity of Self-Diffusion Coefficient....Pages 387-397
Representation Results for Stopping Times in Jump-with-Drift Processes....Pages 399-413
Back Matter....Pages 415-416

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Content:
Front Matter....Pages i-xxxii
Process Level Large Deviations for a Class of Piecewise Homogeneous Random Walks....Pages 1-59
Mutual Singularity of Genealogical Structures of Fleming-Viot and Continuous Branching Processes....Pages 61-83
Regular Conditional Expectations and the Continuum Hypothesis....Pages 85-93
Necessary and Sufficient Conditions for Weak Convergence of One-Dimensional Markov Processes....Pages 95-109
Inverse Subordination of Excessive Functions....Pages 111-131
Jumping Branching Measure-Valued Processes....Pages 133-141
The Boundedness of Branching Markov Processes....Pages 143-152
A Limit Theorem for Weighted Branching Process Trees....Pages 153-166
Loop Condensation Effects in the Behavior of Random Walks....Pages 167-184
On the Stability of Solutions of Stochastic Evolution Equations....Pages 185-197
Harmonic Functions on Riemannian Manifolds: A Probabilistic Approach....Pages 199-207
On a Problem Suggested by A.D. Wentzell....Pages 209-219
Regularity Properties of a Supercritical Superprocess....Pages 221-235
A Lemma on Super-Brownian Motion with Some Applications....Pages 237-251
Sequential Screening of Significant Variables of an Additive Model....Pages 253-265
Brownian Bandits....Pages 267-285
Lyapunov Exponents and Distributions of Magnetic Fields in Dynamo Models....Pages 287-306
The Strong Markov Property of the Support of Super-Brownian Motion....Pages 307-326
Some Results on Random Walks on Groups....Pages 327-332
Diffusions as Integral Curves, or Stratonovich without It?....Pages 333-369
Convex Solutions to Variational Inequalities and Multidimensional Singular Control....Pages 371-386
Regularity of Self-Diffusion Coefficient....Pages 387-397
Representation Results for Stopping Times in Jump-with-Drift Processes....Pages 399-413
Back Matter....Pages 415-416
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