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Backward Coalescence Times for Perfect Simulation of Chains with Infinite Memory

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  04 February 2016

Emilio De Santis  and
Mauro Piccioni
Emilio De Santis*
Affiliation:
Sapienza Università di Roma
Mauro Piccioni*
Affiliation:
Sapienza Università di Roma
*
∗ Postal address: Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy.
∗ Postal address: Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy.
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Abstract

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This paper is devoted to the perfect simulation of a stationary process with an at most countable state space. The process is specified through a kernel, prescribing the probability of the next state conditional to the whole past history. We follow the seminal work of Comets, Fernández and Ferrari (2002), who gave sufficient conditions for the construction of a perfect simulation algorithm. We define backward coalescence times for these kind of processes, which allow us to construct perfect simulation algorithms under weaker conditions than in Comets, Fernández and Ferrari (2002). We discuss how to construct backward coalescence times (i) by means of information depths, taking into account some a priori knowledge about the histories that occur; and (ii) by identifying suitable coalescing events.

Keywords

Perfect simulationcouplingchains with complete connections

MSC classification

Primary: 60G99: None of the above, but in this section 68U20: Simulation 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 319 - 337
Copyright
© Applied Probability Trust 

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