Markov Chains pp 138-171 | Cite as

Introduction to Continuous Time

  • David Freedman

Abstract

Let I be a finite or countably infinite set. A matrix M on I is a function (i, j) → M(i, j) from I × I to the real line. Call M stochastic iff M(i, j) ≧ 0 for all i and j, while Σ j M(i,j) = 1 for all i. Call M substochastic iff M(i, j) ≧ 0 for all i and j, while Σ j M(i, j) ≦ 1 for all i. Matrix multiplication is defined as usual:
$$ MN\left( {i,j} \right) = \sum\nolimits_{{k \in I}} {\,M\left( {i,k} \right)N\left( {k,j} \right)} $$
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Keywords

Ooze 

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Copyright information

© David A. Freedman 1983

Authors and Affiliations

  • David Freedman
    • 1
  1. 1.Department of StatisticsUniversity of CaliforniaBerkeleyUSA

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