Queues And L Vy Fluctuation Theory
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Queues and Lévy Fluctuation Theory
The book provides an extensive introduction to queueing models driven by Lévy-processes as well as a systematic account of the literature on Lévy-driven queues. The objective is to make the reader familiar with the wide set of probabilistic techniques that have been developed over the past decades, including transform-based techniques, martingales, rate-conservation arguments, change-of-measure, importance sampling, and large deviations. On the application side, it demonstrates how Lévy traffic models arise when modelling current queueing-type systems (as communication networks) and includes applications to finance. Queues and Lévy Fluctuation Theory will appeal to postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes.
Information Technologies and Mathematical Modelling. Queueing Theory and Applications
This book constitutes revised selected papers of the 20th International Conference on Information Technologies and Mathematical Modelling, ITMM 2021, named after A.F. Terpugov, held in Tomsk, Russia, in December 2021. Due to the COVID-19 pandemic the conference was held in a virtual mode. The 28 full papers presented in this volume were carefully reviewed and selected from 89 submissions. The conference covers various aspects of information technologies, focusing on queueing theory, stochastic processes, Markov processes, renewal theory, network performance equation and network protocols.
Fluctuations of Lévy Processes with Applications
Author: Andreas E. Kyprianou
language: en
Publisher: Springer Science & Business Media
Release Date: 2014-01-09
Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.