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1 results

  • Yaglom limits can depend on the starting state

  • Part of
  • R. D. Foley, D. R. McDonald
  • Journal:
    Advances in Applied Probability / Volume 50 / Issue 1 / March 2018
    Published online by Cambridge University Press:
    20 March 2018, pp. 1-34
    Print publication:
    March 2018

  • We construct a simple example, surely known to Harry Kesten, of an R-transient Markov chain on a countable state space S ∪ {δ}, where δ is absorbing. The transition matrix K on S is irreducible and strictly substochastic. We determine the Yaglom limit, that is, the limiting conditional behavior given nonabsorption. Each starting state x ∈ S results in a different Yaglom limit. Each Yaglom limit is an R-1-invariant quasi-stationary distribution, where R is the convergence parameter of K. Yaglom limits that depend on the starting state are related to a nontrivial R-1-Martin boundary.