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 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.

I Extensions of Basic Models.- 1 The Solidarity of Markov Renewal Processes.- 2 A Generalization of Semi-Markov Processes.- 3 Quasi-stationary Phenomena for Semi-Markov Processes.- 4 Semi-Markov Random Walks.- 5 Diffusion Approximation for Processes with Semi-Markov Switches.- 6 Approximations for Semi-Markov Single Ion Channel Models.- II Statistical Estimation.- 7 Log-likelihood in Stochastic Processes.- 8 Some Asymptotic Results and Exponential Approximation in Semi-Markov Models.- 9 Markov Renewal Processes and Exponential Families.- 10 On Homogeneity of Two Semi-Markov Samples.- 11 Product-Type Estimator of Convolutions.- 12 Failure Rate Estimation of Semi-Markov Systems.- 13 Estimation for Semi-Markov Manpower Models in a Stochastic Environment.- 14 Semi-Markov Models for Lifetime Data Analysis.- III Non-Homogeneous Models.- 15 Continuous Time Non Homogeneous Semi-Markov Systems.- 16 The Perturbed Non-Homogeneous Semi-Markov System.- IV Queueing Systems Theory.- 17 Semi-Markov Queues with Heavy Tails.- 18 MR Modelling of Poisson Traffic at Intersections Having Separate Turn Lanes.- V Financial Models.- 19 Stochastic Stability and Optimal Control in Insurance Mathematics.- 20 Option Pricing with Semi-Markov Volatility.- VI Controlled Processes & Maintenance.- 21 Applications of Semi-Markov Processes in Reliability and Maintenance.- 22 Controlled Queueing Systems with Recovery Functions.- VII Chromatography & Fluid Mechanics.- 23 Continuous Semi-Markov Models for Chromatography.- 24 The Stress Tensor of the Closed Semi-Markov System. Energy and Entropy.