Perturbed Semi-Markov Type Processes II: Ergodic Theorems for Multi-Alternating Regenerative Processes

ISBN-13: 9783030924010 / Angielski / Miękka / 2023 / 413 str.

Dmitrii Silvestrov

Opis

This book is the second 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 second volume presents a complete classification of ergodic theorems for alternating regenerative processes, including more than twenty-five such theorems. The text addresses new asymptotic recurrent algorithms of phase space reduction for multi-alternating regenerative processes modulating by regularly and singularly perturbed finite semi-Markov processes. It also features a new study of super-long, long, and short time ergodic theorems for these 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.

Spis treści

Preface.- List of symbols.- Introduction.- Part I: Ergodic Theorems for Perturbed Alternating Regenerative Processes.- Ergodic Theorems for Perturbed Regenerative Processes.- Perturbed Alternating Regenerative Processes.- Ergodic Theorems for Regularly Perturbed Alternating Regenerative Processes.- Ergodic Theorems for Regularly Perturbed Alternating Regenerative Processes Compressed in Time.- Super-Long and Long Time Ergodic Theorems for Singularly Perturbed Alternating Regenerative Processes.- Short Time Ergodic Theorems for Singularly Perturbed Alternating Regenerative Processes.- Ergodic Theorems for Singularly Perturbed Alternating Regenerative Processes Compressed in Time.- Ergodic Theorems for Super-Singularly Perturbed Alternating Regenerative Processes.- Part II: Ergodic Theorems for Perturbed Multi-Alternating Regenerative Processes.- Perturbed Multi-Alternating Regenerative Processes.- Time-Space Aggregation of Regeneration Times for Perturbed Multi-Alternating Regenerative Processes.- Embedded Processes for Perturbed Multi-Alternating Regenerative Processes.- Ergodic Theorems for Perturbed Multi-Alternating Regenerative Processes.- Perturbed Renewal Equation.- Supplementary Asymptotic Results.- Methodological and Bibliography Notes.- References.- Index.- 

O autorze

Dmitrii Silvestrov: Candidate of Science [PhD], (1969, Kiev University), Doctor of Science (1972, Kiev University). Professor at Kiev University (1974-1992), Mälardalen University (1999-2009) and Stockholm University from 2009. At present, professor emeritus at Stockholm and Mälardalen Universities. The main areas of research is Stochastic Processes and their Applications. The author of 13 books and more than 170 research papers. Supervised 22 doctoral students who subsequently obtained PhD degrees.