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Probability and Stochastics
This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the applications. In many instances the gist of the problem is introduced in practical, everyday language and then is made precise in mathematical form. The first four chapters are on probability theory: measure and integration, probability spaces, conditional expectations, and the classical limit theorems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and Markov Processes. Special attention is paid to Poisson random measures and their roles ...
Probabilistic Modelling
Probabilistic modelling is the most cost-effective means of performance and reliability evaluation of complex dynamic systems. This self-contained text will be welcomed by students and teachers for its no-nonsense treatment of the basic results and examples of their application. The only mathematical background that is assumed is basic calculus. The necessary fundamentals of probability theory are included, as well as an introduction to renewal, Poisson and Markov processes. Models arising in the fields of manufacturing, computing and communications, involving single or multiple service stations and one or more customer classes, are examined in some detail. Both exact and approximate solution methods are discussed, including recent techniques such as spectral expansion. Special attention is devoted to models of systems subject to breakdowns and repairs. Throughout the book, strong emphasis is placed on explaining the ideas behind the results and helping the reader to use them, making the book ideal for students in computer science, engineering or operations research taking courses in modern system design.
Semi-Markov Models
This book is the result of the International Symposium on Semi Markov Processes and their Applications held on June 4-7, 1984 at the Universite Libre de Bruxelles with the help of the FNRS (Fonds National de la Recherche Scientifique, Belgium), the Ministere de l'Education Nationale (Belgium) and the Bernoulli Society for Mathe matical Statistics and Probability. This international meeting was planned to make a state of the art for the area of semi-Markov theory and its applications, to bring together researchers in this field and to create a platform for open and thorough discussion. Main themes of the Symposium are the first ten sections of this book. The last section presented here gives ...
Reliability Theory and Models
Reliability Theory and Models: Stochastic Failure Models, Optimal Maintenance Policies, Life Testing, and Structures contains the proceedings of a Symposium on Stochastic Failure Models, Replacement and Maintenance Policies, and Accelerated Life Testing, held in Charlotte, North Carolina, on June 24-26, 1983. Contributors discuss the directions for research on stochastic failure models and maintenance and replacement policies, as well as statistical and computational aspects of reliability. This text is divided into five sections and is comprised of 17 chapters; the first of which introduces the reader to Markov and semi-Markov models of deterioration in light of the results on representatio...
Semi-Markov Models and Applications
This book presents a selection of papers presented to the Second Inter national Symposium on Semi-Markov Models: Theory and Applications held in Compiegne (France) in December 1998. This international meeting had the same aim as the first one held in Brussels in 1984 : to make, fourteen years later, the state of the art in the field of semi-Markov processes and their applications, bring together researchers in this field and also to stimulate fruitful discussions. The set of the subjects of the papers presented in Compiegne has a lot of similarities with the preceding Symposium; this shows that the main fields of semi-Markov processes are now well established particularly for basic applicati...
From Markov Jump Processes to Spatial Queues
From Markov Jump Processes to Spatial Queues aims to develop a unified theory of spatial queues that yields concrete results for the performance analysis of mobile communication networks. A particular objective is to develop the most natural generalization of existing concepts (e.g. the BMAP) toward the needs of mobile communication networks. To these belong the spatial distribution of batch arrivals and users in the system as well as time-inhomogeneous (e.g. periodic) arrival intensities and user movements. One of the major recent challenges for the stochastic modelling of communication systems is the emergence of wireless networks, which are used by more and more subscribers today. The mai...
Seminar on Stochastic Processes, 1991
The 1991 Seminar on Stochastic Processes was held at the University of California, Los Angeles, from March 23 through March 25, 1991. This was the eleventh in a series of annual meetings which provide researchers with the opportunity to discuss current work on stochastic processes in an informal and enjoyable atmosphere. Previous seminars were held at Northwestern University, Princeton University, the University of Florida, the University of Virginia, the University of California, San Diego, and the University of British Columbia. Following the successful format of previous years there were five invited lectures. These were given by M. Barlow, G. Lawler, P. March, D. Stroock, M. Talagrand. T...
Fractal Geometry and Stochastics
Fractal geometry is a new and promising field for researchers from different disciplines such as mathematics, physics, chemistry, biology and medicine. It is used to model complicated natural and technical phenomena. The most convincing models contain an element of randomness so that the combination of fractal geometry and stochastics arises in between these two fields. It contains contributions by outstanding mathematicians and is meant to highlight the principal directions of research in the area. The contributors were the main speakers attending the conference "Fractal Geometry and Stochastics" held at Finsterbergen, Germany, in June 1994. This was the first international conference ever to be held on the topic. The book is addressed to mathematicians and other scientists who are interested in the mathematical theory concerning: • Fractal sets and measures • Iterated function systems • Random fractals • Fractals and dynamical systems, and • Harmonic analysis on fractals. The reader will be introduced to the most recent results in these subjects. Researchers and graduate students alike will benefit from the clear expositions.
Stochastic Processes and Related Topics
The aim of this volume is to make accessible to a greater audience papers given at the 10th Winterschool on Stochastic Processes in Siegmundsburg, Germany, March 1994. The papers include developments in stochastic analysis, applications to finance mathematics, Markov processes and diffusion processes, stochastic differential equations and stochastic partial differential equations.
Seminar on Stochastic Processes, 1982
This volume consists of about half of the papers presented during a three-day seminar on stochastic processes held at Northwestern University in March 1982. This was the second of such yearly seminars aimed at bringing together a small group of researchers to discuss their current work in an informal atmosphere. The invited participants in this year's seminar were B. ATKINSON, R. BASS, K. BICHTELER, D. BURKHOLDER, K.L. CHUNG, J.L. DOOB, C. DOLEANS-DADE, H. FOLLMER, R.K. GETOOR, J. GLOVER, J. MITRO, D. MONRAD, E. PERKINS, J. PITMAN, Z. POP-STOJANOVIC, M.J. SHARPE, and J. WALSH. We thank them and the other participants for the lively atmosphere of the seminar. As mentioned above, the present v...
