## Stochastic Processes and Functional Analysis: A Volume of Recent Advances in Honor of M. M. Rao (Google eBook)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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### Contents

For MM Rao | 1 |

An Appreciation of my teacher MM Rao | 3 |

1001 words about Rao | 7 |

A Guide to Life Mathematical and Otherwise | 11 |

Rao and the early Riverside years | 13 |

On MM Rao | 21 |

Reflections on MM Rao | 25 |

Stochastic Analysis and Function Spaces | 27 |

Operator Theoretic Review for Information Channels | 195 |

Pseudoergodicity in Information Channels | 209 |

Connections Between BirthDeath Processes | 219 |

Integrated Gaussian Processes and their Reproducing Kernel Hilbert Spaces | 241 |

Moving Average Representation and Prediction for Multidimensional Harmonizable Processes | 265 |

DoubleLevel Averaging on a Stratified Space | 277 |

The Problem of Optimal Asset Allocation with Stable Distributed Returns | 295 |

Computations for Nonsquare Constants of Orlicz spaces | 349 |

Applications of Sinkhorn balancing to counting problems | 53 |

Existence and Uniqueness | 67 |

Hyperfunctionals and Generalized Distributions | 81 |

Processmeasures and their Stochastic Integral | 119 |

Invariant Sets for Nonlinear Operators | 141 |

The ImmigrationEmigration with Catastrophe Model | 149 |

Approximating Scale Mixtures | 161 |

Their Unitary Operators and Representations | 171 |

Asymptotically Stationary and Related Processes | 363 |

Superlinearity and Weighted Sobolev Spaces | 399 |

Doubly Stochastic Operators and the History of Birkhoffs Problem 111 | 411 |

Classes of Harmonizable Isotropic Random Fields | 441 |

Local Adaptation in NonFluctuating Spatial Patterns | 461 |

Approximating the Time Delay in Coupled van der Pol Oscillators with Delay Coupling | 483 |

### Common terms and phrases

a-stable algebra AMS channel asset assume asymptotically stationary average Banach space bimeasure birth-death chain birth-death process bounded linear operator Brownian motion channel operator consider continuous functions converges convex cyclostationary defined definition denote differential equations doubly stochastic doubly stochastic matrix equivalent ergodic estimate exists extended distributions F01ner sequence finite function spaces Gaussian given harmonizable processes Hence Hilbert space hypemumber hyperfunctional hypernumbers implies infinite integral Krinik Lemma linear operator linear space M.M. Rao mapping martingale Math Mathematics mean measure norm numerical sequence obtained optimal allocation Orlicz spaces Pa(X parameter portfolio positive probability process-measure Proof properties Proposition Rachev random element random field random variable real hypernumbers real numbers representation result RKHS sample paths satisfies solution species spectral stable distributed stationary channel stationary processes stochastic operators Stochastic Processes strongly harmonizable summable Theorem theory tion topology values vector weakly harmonizable

### Popular passages

Page x - Stochastic Control Theory and Stochastic Differential Systems, Lecture Notes in Control and Information Sciences, 16 (1979), 527-538, Springer Verlag.

Page iii - Attended the winter and summer meetings of the American Mathematical Society and the Mathematical Association of America...

Page 397 - Fourier transforms of noncommutative analogues of vector measures and bimeasures with applications to stochastic processes 6-12531 Yttnen, R.