Stochastic Processes and Functional Analysis: In Honor of M. M. Rao (Lecture Notes in Pure and Applied Mathematics)

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Overview

This extraordinary compilation is an expansion of the recent American Mathematical Society Special Session celebrating M. M. Rao's distinguished career and includes most of the presented papers as well as ancillary contributions from session invitees. This book shows the effectiveness of abstract analysis for solving fundamental problems of stochastic theory, specifically the use of functional analytic methods for elucidating stochastic processes, as made manifest in M. M. Rao's prolific research achievements. Featuring a biography of M. M. Rao, a complete bibliography of his published works, and meditations from former students, the book includes contributions from over 30 notable researchers.

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Product Details

Table of Contents

Preface
Biography of M. M. Rao
Published Writings of M. M. Rao
Ph.D. Theses Completed Under the Direction of M. M. Rao
Contributors
For M. M. Rao 1
An Appreciation of My Teacher, M. M. Rao 3
1001 Words About Rao 7
A Guide to Life, Mathematical and Otherwise 11
Rao and the Early Riverside Years 13
On M. M. Rao 21
Reflections on M. M. Rao 25
1 Stochastic Analysis and Function Spaces 27
2 Applications of Sinkhorn Balancing to Counting Problems 53
3 Zakai Equation of Nonlinear Filtering with Ornstein-Uhlenbeck Noise: Existence and Uniqueness 67
4 Hyperfunctionals and Generalized Distributions 81
5 Process-Measures and Their Stochastic Integral 119
6 Invariant Sets for Nonlinear Operators 141
7 The Immigration-Emigration with Catastrophe Model 149
8 Approximating Scale Mixtures 161
9 Cyclostationary Arrays: Their Unitary Operators and Representations 171
10 Operator Theoretic Review for Information Channels 195
11 Pseudoergodicity in Information Channels 209
12 Connections Between Birth-Death Processes 219
13 Integrated Gaussian Processes and Their Reproducing Kernel Hilbert Spaces 241
14 Moving Average Representation and Prediction for Multidimensional Harmonizable Processes 265
15 Double-Level Averaging on a Stratified Space 277
16 The Problem of Optimal Asset Allocation with Stable Distributed Returns 295
17 Computations for Nonsquare Constants of Orlicz Spaces 349
18 Asymptotically Stationary and Related Processes 363
19 Superlinearity and Weighted Sobolev Spaces 399
20 Doubly Stochastic Operators and the History of Birkhoff's Problem 111 411
21 Classes of Harmonizable Isotropic Random Fields 441
22 On Geographically-Uniform Coevolution: Local Adaptation in Non-fluctuating Spatial Patterns 461
23 Approximating the Time Delay in Coupled van der Pol Oscillators with Delay Coupling 483
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