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This book explores various renewal processes in the context of probability theory, uncertainty theory and chance theory. It also covers the applications of these renewal processes in maintenance models and insurance risk models. The methods used to derive the limit of the renewal rate, the reward rate, and the availability rate are of particular interest, as they can easily be extended to the derivation of other models. Its comprehensive and systematic treatment of renewal processes, renewal reward processes and the alternating renewal process is one of the book's major features, making it particularly valuable for readers who are interested in learning about renewal theory. Given its scope, the book will benefit researchers, engineers, and graduate students in the fields of mathematics, information science, operations research, industrial engineering, etc.
List of contents
Probability Theory.- Stochastic Renewal Processes.- Uncertainty Theory.- Uncertain Renewal Processes.- Chance Theory.- Uncertain Random Renewal Processes.
About the author
Dr. Kai Yao is currently an Associate Professor at the School of Economics and Management, University of Chinese Academy of Sciences. He has published about 50 papers in international journals, which have been cited more than 1700 times in Google Scholar. He serves as an associate editor for Fuzzy Optimization and Decision Making, and as a guest editor for several other journals, including Soft Computing and the Journal of Intelligent Manufacturing. His research interests include Uncertainty Theory, Renewal Theory, and Uncertain Differential Equations.
Summary
This book explores various renewal processes in the context of probability theory, uncertainty theory and chance theory. It also covers the applications of these renewal processes in maintenance models and insurance risk models. The methods used to derive the limit of the renewal rate, the reward rate, and the availability rate are of particular interest, as they can easily be extended to the derivation of other models. Its comprehensive and systematic treatment of renewal processes, renewal reward processes and the alternating renewal process is one of the book’s major features, making it particularly valuable for readers who are interested in learning about renewal theory. Given its scope, the book will benefit researchers, engineers, and graduate students in the fields of mathematics, information science, operations research, industrial engineering, etc.
Additional text
“The book is self-contained and is suitable for researchers and students in the field of applied mathematics, operations research, engineering and management sciences. There is certainly a future for the research in uncertainty!” (Edward Omey, zbMATH 1448.60004, 2020)
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"The book is self-contained and is suitable for researchers and students in the field of applied mathematics, operations research, engineering and management sciences. There is certainly a future for the research in uncertainty!" (Edward Omey, zbMATH 1448.60004, 2020)
