More Examples for the Stable Case

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

Chapter 8 in Markov Chains, 1983, pp 252-296 from Springer

Abstract: Abstract Let P be a standard stochastic semigroup on the countably infinite set I. Suppose a, b, c are distinct elements of I. As usual, Q = P′(0) exists by (5.21). If Q(a, b) > 0 or if Q(a, c) > 0, then P(t, a, b)/P(t, a, c) converges as t → 0, namely to Q(a, b)/Q(a, c). If P is uniform, then P is analytic by (5.29), so the convergence holds by l’Hôpital (10.78 and 80). Lester Dubins asked me whether the convergence held in general.

Keywords: Stationary Transition; Markov Chain; Sample Function; Stable Case; Discrete Time Markov Chain (search for similar items in EconPapers)
Date: 1983
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DOI: 10.1007/978-1-4612-5500-0_8

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