Stochastic Processes and Functional Analysis: New Perspectives (Contemporary Mathematics, 774)

✍ Scribed by Randall J. Swift (editor), Alan Krinik (editor), Jennifer M. Switkes (editor), Jason H. Park (editor)

• Publisher: AMS
• Year: 2021
• Tongue: English
• Leaves: 286
• Category: Library

✦ Synopsis

A November 2019 special session in Riverside, California focused on the key role in abstract analysis plays in simplifying and solving fundamental problems in stochastic theory. The 13 mathematical papers discuss such matters as sufficient conditions for Lorentz ordering with common finite support, nonlinear parabolic equations with Robin boundary conditions and Hardy-Leray type inequalities, explicit transient probability of various Markov models, Eulerian polynomials and quasi-birth-death processes with time-varying-periodic rates, and the exponential-dual matrix method: applications to Markov chain analysis. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)

✦ Table of 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 𝑋 and 𝑌 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
References
How strong can the Parrondo effect be? II
1. Introduction
2. SLLN for random sequences of games
3. Stationary distribution of the random walk on the 𝑛-cycle
4. Evaluation of rate of profit
References
Binary response models comparison using the 𝛼-Chernoff divergence measure and exponential integral functions
1. Introduction
2. Exponential family of models
3. The 𝛼-Chernoff divergence
4. First family of models
5. Exponential integral function and 𝛼-Chernoff divergence
6. Second family of models
7. Interpretations, explanations and applications
References
Nonlinear parabolic equations with Robin boundary conditions and Hardy-Leray type inequalities
1. Introduction
2. Main result
3. Improved Hardy type inequalities and applications
4. Applications
5. The one and two-dimensional cases
References
Banach space valued weak second order stochastic processes
1. Introduction
2. The spaces 𝐵(𝔘,ℌ) and 𝔅(𝔘,𝔘)
3. 𝐵(𝔘,ℌ)-valued measures
4. 𝐵(𝔘,𝔘)-valued measures and bimeasures
5. 𝐵(𝔘,ℌ)-valued processes
References
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
Acknowledgments
References
On the use of Markovian stick-breaking priors
1. Introduction
2. Definition of the Markovian stick-breaking process
3. Results on moments, posterior distribution, and consistency
4. On use of the MSB(𝐺) measure as a prior
5. Proof of Theorem 4
Acknowledgments
References
Eulerian polynomials and Quasi-Birth-Death processes with time-varying-periodic rates
1. Introduction
2. The approach
3. Single-server queue
4. Single-server priority queue with finite Buffer
5. Conclusion
Acknowledgment
References
Random measure algebras
1. Introduction
2. Preliminaries
3. A convolution by covariance method
4. O-dot product and convolution of bimeasures
5. Convolution by strict Morse-Transue integral
References
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
References
The exponential-dual matrix method: Applications to Markov chain analysis
1. Introduction
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
1. Introduction
2. A generalized interacting species model
3. Stochastic interacting species model
4. Moment closure using normal distribution
5. Moment closure using lognormal distribution
6. Conclusions
References
Back Cover