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.
Author(s): Alan C. Krinik, Randall J. Swift
Series: Lecture Notes in Pure and Applied Mathematics
Edition: 1
Year: 2004
Language: English
Pages: 400
Preface......Page 9
Biography of M. M. Rao......Page 11
Published Writings of M. M. Rao......Page 13
Ph.D. Theses Completed Under the Direction of M.M. Rao......Page 21
Contents......Page 23
Contributors......Page 27
For M.M. Rao......Page 29
An Appreciation of my teacher, M.M. Rao......Page 31
1001 words about Rao......Page 35
A Guide to Life, Mathematical and Otherwise......Page 39
Rao and the early Riverside years......Page 41
On M.M. Rao......Page 49
Reflections on M.M. Rao......Page 53
Stochastic Analysis and Function Spaces......Page 55
Applications of Sinkhorn balancing to counting problems......Page 81
Zakai equation of nonlinear filtering with Ornstein-Uhlenbeck noise: Existence and Uniqueness......Page 95
Hyperfunctionals and Generalized Distributions......Page 109
Process-measures and their Stochastic Integral......Page 147
Invariant Sets for Nonlinear Operators......Page 169
The Immigration-Emigration with Catastrophe Model......Page 177
Approximating Scale Mixtures......Page 189
Cyclostationary Arrays: Their Unitary Operators and Representations......Page 199
Operator Theoretic Review for Information Channels......Page 223
Pseudoergodicity in Information Channels......Page 237
Connections Between Birth-Death Processes......Page 247
Integrated Gaussian Processes and their Reproducing Kernel Hilbert Spaces......Page 269
Moving Average Representation and Prediction for Multidimensional Harmonizable Processes......Page 293
Double-Level Averaging on a Stratified Space......Page 305
The Problem of Optimal Asset Allocation with Stable Distributed Returns......Page 323
Computations for Nonsquare Constants of Orlicz spaces......Page 377
Asymptotically Stationary and Related Processes......Page 391
Superlinearity and Weighted Sobolev Spaces......Page 427
Doubly Stochastic Operators and the History of Birkhoff's Problem 111......Page 439
Classes of Harmonizable Isotropic Random Fields......Page 469
On Geographically-Uniform Coevolution: Local Adaptation in Non-Fluctuating Spatial Patterns......Page 489
Approximating the Time Delay in Coupled van der Pol Oscillators with Delay Coupling......Page 511
