Journal of Applied Probability

Backward coalescence times for perfect simulation of chains with infinite memory

Emilio De Santis and Mauro Piccioni

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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.

Article information

J. Appl. Probab., Volume 49, Number 2 (2012), 319-337.

First available in Project Euclid: 16 June 2012

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Zentralblatt MATH identifier

Primary: 60G99: None of the above, but in this section 68U20: Simulation [See also 65Cxx] 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Perfect simulation coupling chains with complete connections


De Santis, Emilio; Piccioni, Mauro. Backward coalescence times for perfect simulation of chains with infinite memory. J. Appl. Probab. 49 (2012), no. 2, 319--337. doi:10.1239/jap/1339878789.

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