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1 results

  • Exact and ordinary lumpability in finite Markov chains

  • Part of
  • Peter Buchholz
  • Journal:
    Journal of Applied Probability / Volume 31 / Issue 1 / March 1994
    Published online by Cambridge University Press:
    14 July 2016, pp. 59-75
    Print publication:
    March 1994

  • Exact and ordinary lumpability in finite Markov chains is considered. Both concepts naturally define an aggregation of the Markov chain yielding an aggregated chain that allows the exact determination of several stationary and transient results for the original chain. We show which quantities can be determined without an error from the aggregated process and describe methods to calculate bounds on the remaining results. Furthermore, the concept of lumpability is extended to near lumpability yielding approximative aggregation.