Stochastic Processes and Functional Analysis

An expansion on the recent American Mathematical Society Special Session celebrating M. M. Rao's distinguished career, this extraordinary compilation includes most of the presented papers as well as ancillary contributions from session invitees. This book decisively 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 Rao's prolific achievements.

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

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