Stochastic Processes and Functional Analysis : New Perspectives.

Format:

Book

Author/Creator:

Swift, Randall J.

Contributor:

Krinik, Alan.

Switkes, Jennifer M.

Series:

Contemporary Mathematics

Contemporary Mathematics ; v.774

Language:

English

Subjects (All):

Stochastic processes--Congresses.

Stochastic processes.

Functional analysis--Congresses.

Functional analysis.

Rao, M. M. (Malempati Madhusudana), 1929-.

Rao, M. M.

Physical Description:

1 online resource (286 pages)

Edition:

1st ed.

Other Title:

Stochastic Processes and Functional Analysis

Place of Publication:

Providence : American Mathematical Society, 2021.

Summary:

This volume contains the proceedings of the AMS Special Session on Celebrating M. M. Rao's Many Mathematical Contributions as he Turns 90 Years Old, held from November 9-10, 2019, at the University of California, Riverside, California.The articles show the effectiveness of abstract analysis for solving fundamental problems of stochastic theory, specifically the use of functional analytic methods for elucidating stochastic processes and their applications. The volume also includes a biography of M. M. Rao and the list of his publications.

Contents:

Cover

Title page

Contents

Preface

Stochastic Equations

Biography of M. M. Rao

Published Writings of M. M. Rao

Ph.D. Theses Completed Under the Direction of M.M. Rao

Celebrating M.M. Rao's Many Mathematical Contributions

Sufficient conditions for Lorenz ordering with common finite support

1. Introduction

2. The usual Lorenz order and the role of Robin Hood

3. Other partial orders defined on ℒ₊

4. When and have common finite support

5. Robin Hood's role in the common finite support setting

6. Are the usual sufficient conditions for Lorenz ordering useful in the common finite support situation?

7. Discussion

References

Ergodicity and steady state analysis for interference queueing networks

1. Introduction and model

2. Main results

3. Proof of Theorem 2.1 and Corollary 2.2

4. Proof of Theorem 2.3

Acknowledgments

How strong can the Parrondo effect be? II

2. SLLN for random sequences of games

3. Stationary distribution of the random walk on the -cycle

4. Evaluation of rate of profit

Binary response models comparison using the -Chernoff divergence measure and exponential integral functions

2. Exponential family of models

3. The -Chernoff divergence

4. First family of models

5. Exponential integral function and -Chernoff divergence

6. Second family of models

7. Interpretations, explanations and applications

Nonlinear parabolic equations with Robin boundary conditions and Hardy-Leray type inequalities

2. Main result

3. Improved Hardy type inequalities and applications

4. Applications

5. The one and two-dimensional cases

Banach space valued weak second order stochastic processes

1. Introduction.

2. The spaces ( ,ℌ) and ( , *)

3. ( ,ℌ)-valued measures

4. ( , *)-valued measures and bimeasures

5. ( ,ℌ)-valued processes

Explicit transient probabilities of various Markov models

1. Introduction and summary

2. Matrix results

3. Strip probabilities and ballot box problems

4. Birth-death models with catastrophes

5. Odd tridiagonal matrices having constant main diagonal entries and alternating entries on the remaining diagonals

6. Circulant matrices

Appendix A. Appendix

On the use of Markovian stick-breaking priors

2. Definition of the Markovian stick-breaking process

3. Results on moments, posterior distribution, and consistency

4. On use of the MSB( ) measure as a prior

5. Proof of Theorem 4

Eulerian polynomials and Quasi-Birth-Death processes with time-varying-periodic rates

2. The approach

3. Single-server queue

4. Single-server priority queue with finite Buffer

5. Conclusion

Acknowledgment

Random measure algebras

2. Preliminaries

3. A convolution by covariance method

4. O-dot product and convolution of bimeasures

5. Convolution by strict Morse-Transue integral

From additive to second-order processes

1. Counting processes

2. Random measures

3. Harmonic analysis as a bridge

4. Stable processes

5. Second order processes

The exponential-dual matrix method: Applications to Markov chain analysis

2. Uniformization

3. Stochastic duality

4. Transient analysis using uniformization and duality

5. Generalization of the stochastic-dual: The exponential-dual matrix

6. Conclusions

References.

Two moment closure techniques for an interacting species model

2. A generalized interacting species model

3. Stochastic interacting species model

4. Moment closure using normal distribution

5. Moment closure using lognormal distribution

Back Cover.

Notes:

Description based on publisher supplied metadata and other sources.

"AMS Special Session on Celebrating M.M. Rao's Many Mathematical Contributions as he Turns 90 Years Old November 9-10, 2019 University of California Riverside, California

Includes bibliographical references."

ISBN:

9781470467166

147046716X

OCLC:

1284289962