فرایندهای تصادفی و تحلیل تابعی: دیدگاه‌های جدید

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) 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 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. -- Provided by publisher