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Discrete Approximation of Markovprocesses by Markovchains

In: Probability and Statistical Inference

Author

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  • Johannes Adler

    (Technische Universität Wien, Institut für Statistik und Wahrscheinlichkeitstheorie)

Abstract

The concept of discrete convergence, introduced by Stummel [3] is the frame within the convergence of semigroups with discrete parameter to a semigroup with continous parameter can be studied, cf. Trotter [4] and Kurtz [2]. On the other hand, discrete convergence gives us the frame within we can define weak convergence of a sequence of space-time discrete Markovchains to a space-time continous Markovprocess. The connection is studied between discrete convergence of Markov-processes and discrete convergence of the corresponding semigroups and infinitesimal operators.

Suggested Citation

  • Johannes Adler, 1982. "Discrete Approximation of Markovprocesses by Markovchains," Springer Books, in: Wilfried Grossmann & Georg Ch. Pflug & Wolfgang Wertz (ed.), Probability and Statistical Inference, pages 1-11, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-7840-9_1
    DOI: 10.1007/978-94-009-7840-9_1
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