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  1. Continuous-time Markov chains : an applications-oriented approach

    Anderson, William J. (William James), 1943-
    New York : Springer-Verlag, c1991.

    Continuous time parameter Markov chains have been useful for modelling various random phenomena occurring in queueing theory, genetics, demography, epidemiology, and competing populations. This book is about those aspects of the theory of continuous time Markov chains which are useful in applications to such areas. It studies continuous time Markov chains through the transition function and corresponding q-matrix, rather than sample paths. A discussion of birth and death processes, including the Stieltjes moment problem, and the Karlin-McGregor method of solution of the birth and death processes and multi-dimensional population processes is included, and there is a detailed bibliography. Virtually all of this material is appearing in book form for the first time. This monograph on probability and statistics, medical statistics, documentation, biomathematics, and genetics is intended for applied probabilists, researchers in queueing theory, genetics, demography, epidemiology, and competing populations.

  2. ARMA model identification

    Choi, ByoungSeon
    New York : Springer-Verlag, c1992.

    During the past two decades, considerable progress has been made in statistical time series analysis. The aim of this book is to present a survey of one of the most active areas in this field: the identification of autoregressive moving-average models, i.e., determining their orders. Readers are assumed to have already taken one course on time series analysis as might be offered in a graduate course, but otherwise this account is self-contained. The main topics covered include: Box-Jenkins' method, inverse autocorrelation functions, penalty function identification such as AIC, BIC techiques and Hannan and Quinn's method, instrumental regression, and a range of pattern identification methods. Rather than cover all the methods in detail, the emphasis is on exploring the fundamental ideas underlying them. References are given to the research literature and as a result, all those engaged, in research in this subject should find this a useful aid to their work.

  3. Aspects of Risk Theory

    Grandell, Jan.
    New York, NY : Springer New York, 1991.

    Risk theory, which deals with stochastic models of an insurance business, is a classical application of probability theory. The fundamental problem in risk theory is to investigate the ruin possibility of the risk business. Traditionally the occurrence of the claims is described by a Poisson process and the cost of the claims by a sequence of random variables. This book is a treatise of risk theory with emphasis on models where the occurrence of the claims is described by more general point processes than the Poisson process, such as renewal processes, Cox processes and general stationary point processes. In the Cox case the possibility of risk fluctuation is explicitly taken into account. The presentation is based on modern probabilistic methods rather than on analytic methods. The theory is accompanied with discussions on practical evaluation of ruin probabilities and statistical estimation. Many numerical illustrations of the results are given.

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