Perturbed Semi-Markov Type Processes I
Autor Dmitrii Silvestroven Limba Engleză Hardback – 29 mar 2022
This book is the first volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation.
The first volume presents necessary and sufficient conditions for weak convergence for first-rare-event times and convergence in the topology J for first-rare-event processes defined on regularly perturbed finite Markov chains and semi-Markov processes. The text introduces new asymptotic recurrent algorithms of phase space reduction. It also addresses both effective conditions of weak convergence for distributions of hitting times as well as convergence of expectations of hitting times for regularly and singularly perturbed finite Markov chains and semi-Markov processes.
The book also contains a comprehensive bibliography of major works in the field. It provides an effective reference for both graduate students as well as theoretical and applied researchers studying stochastic processes and their applications.
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Specificații
ISBN-13: 9783030924027
ISBN-10: 3030924025
Pagini: 420
Ilustrații: XVII, 401 p. 8 illus., 3 illus. in color.
Dimensiuni: 160 x 241 x 29 mm
Greutate: 0.74 kg
Ediția:1st ed. 2022
Editura: Springer
Locul publicării:Cham, Switzerland
ISBN-10: 3030924025
Pagini: 420
Ilustrații: XVII, 401 p. 8 illus., 3 illus. in color.
Dimensiuni: 160 x 241 x 29 mm
Greutate: 0.74 kg
Ediția:1st ed. 2022
Editura: Springer
Locul publicării:Cham, Switzerland
Cuprins
Preface.- List of symbols.- Introduction.- Part I: First-Rare-Event Times for Regularly Perturbed Semi-Markov Processes.- Flows of Rare Events for Regularly Perturbed Semi-Markov Processes.- Generalizations of Limit Theorems for First-Rare-Event Times.- First-Rare-Event Times for Perturbed Risk Processes.- First-Rare-Event Times for Perturbed Closed Queuing Systems.- First-Rare-Event Times for Perturbed M/M-Type Queuing Systems.- Part II: Hitting Times and Phase Space Reduction for Perturbed Semi-Markov Processes.- Asymptotically Comparable Functions.- Perturbed Semi-Markov Processes and Reduction of Phase Space.- Asymptotics of Hitting Times for Perturbed Semi-Markov Processes.- Asymptotics for Expectations of Hitting Times for Perturbed Semi-Markov Processes.- Generalizations and Examples of Limit Theorems for Hitting Times.- Limit Theorems for Randomly Stopped Stochastic Processes.- Methodological and Bibliographical Notes.- References.- Index.
Recenzii
“The book is concluded with the most up-to-date references, which complement these topics for the interested reader. This book is well-organized and expansive. … The results are properly motivated with precise, detailed proofs provided. This book is a must-have item for researchers interested in limit theorems as well as for other probability theorists.” (Steve Drekic, Mathematical Reviews, February, 2023)
Notă biografică
Dmitrii Silvestrov graduated from Kiev University (1968, Mathematics), Candidate of Science [PhD], (1969, Mathematical Statistics), and Doctor of Science (1972, Mathematical Statistics). Awarded the Prize of the Moscow Mathematical Society (1973) and the Ukrainian Ostrovsky Prize (1977) for work on stochastic processes. Lecturer and Senior Lecturer (1970-1974), Professor (1974-1992, Department of Probability and Mathematical Statistics) and Head of the Statistical Research Centre (1980-1990) at Kiev University. Guest scientist at Umeå University (1991-1992), Senior lecturer at Luleå University of Technology (1992-1994) and at Umeå University (1994-1999). Visiting professor at the Hebrew University of Jerusalem (1993), University of Turku (1998), and University of Rome "La Sapienza" (2015). Professor at the Mälardalen University from 1999 (Emeritus Professor from 2012) and Stockholm University from 2009 (Emeritus Professor from 2016). Member of the editorial boards of the journals "Theory of Probability and Mathematical Statistics" and "Theory of Stochastic Processes". Coordinator of the four EU Tempus Projects. The main research areas are stochastic processes, actuarial and financial mathematics, and statistical software. Author of 13 books and more than 170 research papers. Supervised 22 doctoral students who subsequently obtained PhD degrees.
Textul de pe ultima copertă
This book is the first volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation.
The first volume presents necessary and sufficient conditions for weak convergence for first-rare-event times and convergence in the topology J for first-rare-event processes defined on regularly perturbed finite Markov chains and semi-Markov processes. The text introduces new asymptotic recurrent algorithms of phase space reduction. It also addresses both effective conditions of weak convergence for distributions of hitting times as well as convergence of expectations of hitting times for regularly and singularly perturbed finite Markov chains and semi-Markov processes.
The book also contains a comprehensive bibliography of major works in the field. It providesan effective reference for both graduate students as well as theoretical and applied researchers studying stochastic processes and their applications.
Caracteristici
Provides a snapshot of a popular emerging topic Presents new research and contextual literature review Suitable for researchers and mixed-level classes