Background on Probability and Statistics (2024)

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  • Peter E. Kloeden4,
  • Eckhard Platen5 &
  • Henri Schurz6

Part of the book series: Universitext ((UTX))

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Abstract

Some basic facts from probability and statistics, including methods for the generation and testing of random variables, are reviewed in this chapter. Even if the reader is familiar with probability theory, this chapter should be perused, at least, because it provides an explanation of how the book is organized, in particular the computer programs, as well as hints and useful background remarks.

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Literature for Chapter 1

  • Karlin & Taylor (1970,1981), Chung (1975) and Shiryayev (1984) provide comprehensive introductions to probability theory. A computational approach to elem entary probability and basic st atistics can be found in Groeneveld (1979). Introductions and su rveys to pseudo-random number generation are given in Rubinstein (1981), Ripley (1983), Morgan (1984), Marsaglia (1985) and Niederreiter (1992). Random number generation on supercomputers including laggedFibonacci generators is considered in Petersen (1988) and Anderson (1990). Markov chains are treated, e.g., in Chung (1975), Karlin & Taylor (1970) and Shiryayev (1984). For further information on the Wiener process and related questions see, e.g., Hida (1980), Karatzas & Shreve (1988).

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Authors and Affiliations

  1. Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, 60054, Frankfurt am Main, Germany

    Peter E. Kloeden

  2. Department of Mathematical Sciences, University of Technology, Broadway, NSW, 2007, Australia

    Eckhard Platen

  3. Department of Mathematics, Southern Illinois University, Carbondale, IL, 62901-4408, USA

    Henri Schurz

Authors

  1. Peter E. Kloeden

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  2. Eckhard Platen

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  3. Henri Schurz

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© 1994 Springer-Verlag Berlin Heidelberg

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Kloeden, P.E., Platen, E., Schurz, H. (1994). Background on Probability and Statistics. In: Numerical Solution of SDE Through Computer Experiments. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57913-4_1

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  • DOI: https://doi.org/10.1007/978-3-642-57913-4_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57074-5

  • Online ISBN: 978-3-642-57913-4

  • eBook Packages: Springer Book Archive

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Background on Probability and Statistics (2024)
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