The Boundary

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

Chapter 4 in Markov Chains, 1983, pp 111-137 from Springer

Abstract: Abstract This chapter is based on work of Blackwell (1955, 1962), Doob (1959), Feller (1956), and Hunt (1960). Let P be a substochastic matrix on I: that is, P(i, j) ≧ 0 and Σ j ∈ I P(i, j)≦1. Let P 0 be the identity matrix, and Σ n=0 ∞ P n . Suppose G 0 for all i ∈ I. Here pG(i) means Σ j ∈ I P(j)G(j, i). A function h on I is excessive iff: 1 $$ h \geqq 0 $$ 2 $$ \sum\nolimits_{{i \in I}} {p(i)h(i) = 1} $$ and 3 $$ \sum\nolimits_{{i \in I}} {P(i,j)h(j) \leqq h(i)} $$ for all i ∈ I. Check, h(i)

Keywords: Stationary Transition; Markov Chain; Random Walk; Measurable Subset; White Ball (search for similar items in EconPapers)
Date: 1983
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DOI: 10.1007/978-1-4612-5500-0_4

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