Synopses & Reviews
It is now clear that semi-Markov processes play an increasingly crucial role in business and industry; this is partially due to the fact that, with the powerful mathematical software now existing, the numerical treatment of basic integral equations is easier and so leads to more concrete applications; moreover the development of topics such as non-homogeneous models and statistical estimation make it possible to construct more adequate models of real-life problems and to calibrate the basic parameters of the models more accurately from real data. This book presents many original models that are or could be truly useful for applications in real-life problems, and the editor hopes that it will contribute to the stimulation of new interactions between the theoretical development and the applications of semi-Markov models. Audience: This book should constitute a basic reference for researchers of this important field of stochastic modelling.
Synopsis
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 applications in Reliability and Maintenance, Biomedicine, Queue ing, Control processes and production. A growing field is the one of insurance and finance but this is not really a surprising fact as the problem of pricing derivative products represents now a crucial problem in economics and finance. For example, stochastic models can be applied to financial and insur ance models as we have to evaluate the uncertainty of the future market behavior in order, firstly, to propose different measures for important risks such as the interest risk, the risk of default or the risk of catas trophe and secondly, to describe how to act in order to optimize the situation in time. Recently, the concept of VaR (Value at Risk) was "discovered" in portfolio theory enlarging so the fundamental model of Markowitz."
Table of Contents
Preface.
Part I: Extensions of Basic Models. 1. The Solidarity of Markov Renewal Processes;
R. Pyke. 2. A Generalization of Semi-Markov Processes;
M. Iosifescu. 3. Quasi-stationary Phenomena for Semi-Markov Processes;
M. Gyllenberg, D.S. Silvestrov. 4. Semi-Markov Random Walks;
V.S. Korolyuk. 5. Diffusion Approximation for Processes with Semi-Markov Switches;
V.V. Anisimov. 6. Approximations for Semi-Markov Single Ion Channel Models;
S.M. Pitts. Part II: Statistical Estimation. 7. Log-likelihood in Stochastic Processes;
G.G. Rousas, D. Bhattacharya. 8. Some Asymptotic Results and Exponential Approximation in Semi-Markov Models;
G.G. Roussas, D. Bhattacharya. 9. Markov Renewal Processes and Exponential Families;
V.T. Stefanov. 10. On Homogeneity of Two Semi-Markov Samples;
L. Afanasyeva, P. Radchenko. 11. Product-Type Estimator of Convolutions;
I. Gertsbakh, I. Spungin. 12. Failure Rate Estimation of Semi-Markov Systems;
B. Ouhbi, N. Limnios. 13. Estimation for Semi-Markov Manpower Models in a Stochastic Environment;
S. McClean, E. Montgomery. 14. Semi-Markov Models for Lifetime Data Analysis;
R. Pérez-Ocón, et al. Part III: Non-Homogeneous Models. 15. Continuous Time Non Homogeneous Semi-Markov Systems;
A.A. Papadopoulou, P.C.G. Vassiliou. 16. The Perturbed Non-Homogeneous Semi-Markov System;
P.C.G. Vassiliou, H. Tsakiridou. Part IV: Queueing Systems Theory. 17. Semi-Markov Queues with Heavy Tails;
S. Asmussen. 18. MR Modelling of Poisson Traffic at Intersections Having Separate Turn Lanes;
R. Gideon, R. Pyke. Part V: Financial Models. 19. Stochastic Stability and Optimal Control in Insurance Mathematics;
A. Swishchuk. 20. Option Pricing with Semi-Markov Volatility;
J. Janssen, et al. Part VI: Controlled Processes & Maintenance. 21. Applications of Semi-Markov Processes in Reliability and Maintenance;
M. Abdel-Hameed. 22. Controlled Queueing Systems with Recovery Functions;
T. Dohi, et al. Part VII: Chromatography & Fluid Mechanics. 23. Continuous Semi-Markov Models for Chromatography;
B.P. Harlamov. 24. The Stress Tensor of the Closed Semi-Markov System. Energy and Entropy;
G.M. Tsaklidis. Index.