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1 results

  • The calculation of limit probabilities for denumerable Markov processes from infinitesimal properties

  • Richard L. Tweedie
  • Journal:
    Journal of Applied Probability / Volume 10 / Issue 1 / March 1973
    Published online by Cambridge University Press:
    14 July 2016, pp. 84-99
    Print publication:
    March 1973

  • The problem considered is that of estimating the limit probability distribution (equilibrium distribution) πof a denumerable continuous time Markov process using only the matrix Q of derivatives of transition functions at the origin. We utilise relationships between the limit vector πand invariant measures for the jump-chain of the process (whose transition matrix we write P∗), and apply truncation theorems from Tweedie (1971) to P∗. When Q is regular, we derive algorithms for estimating πfrom truncations of Q; these extend results in Tweedie (1971), Section 4, from q-bounded processes to arbitrary regular processes. Finally, we show that this method can be extended even to non-regular chains of a certain type.