Introduction to Continuous Time

David Freedman
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David Freedman: University of California, Department of Statistics

Chapter 5 in Markov Chains, 1983, pp 138-171 from Springer

Abstract: 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: $$ MN\left( {i,j} \right) = \sum\nolimits_{{k \in I}} {\,M\left( {i,k} \right)N\left( {k,j} \right)} $$ .

Keywords: Stationary Transition; Markov Chain; Continuous Time; Step Function; Sample Function (search for similar items in EconPapers)
Date: 1983
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DOI: 10.1007/978-1-4612-5500-0_5

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