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UNIFORMIZATION FOR -POSITIVE MARKOV CHAINS
 

Summary: UNIFORMIZATION FOR
-POSITIVE MARKOV CHAINS
Richard J. Boucherie
Department of Econometrics, Universiteit van Amsterdam
Roetersstraat 11, 1018 WB Amsterdam, The Netherlands
boucheri@butler.fee.uva.nl
Erik A. van Doorn
Faculty of Applied Mathematics, University of Twente
P.O. Box 217, 7500 AE Enschede, The Netherlands
doorn@math.utwente.nl
Abstract. We show that a variant of the uniformization method for the nu-
merical calculation of transient state probabilities of positive recurrent Markov
chains, in which the truncation error can be made arbitrarily small uniformly
over time, can be extended to -positive Markov chains.
Keywords: uniformization, truncation error, -positive recurrence
1 INTRODUCTION
The uniformization or randomization method, introduced by Jensen in [10],
is a technique for obtaining transient state probabilities of continuous-time
Markov chains. The method relates the evolution of a continuous-time Markov
chain to the evolution of a Markov jump chain in which the jump epochs are

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering