2,598 research outputs found
Stochastically Perturbed Chains of Variable Memory
In this paper, we study inference for chains of variable order under two
distinct contamination regimes. Consider we have a chain of variable memory on
a finite alphabet containing zero. At each instant of time an independent coin
is flipped and if it turns head a contamination occurs. In the first regime a
zero is read independent of the value of the chain. In the second regime, the
value of another chain of variable memory is observed instead of the original
one. Our results state that the difference between the transition probabilities
of the original process and the corresponding ones of the contaminated process
may be bounded above uniformly. Moreover, if the contamination probability is
small enough, using a version of the Context algorithm we are able to recover
the context tree of the original process through a contaminated sample
Perfect simulation of a coupling achieving the -distance between ordered pairs of binary chains of infinite order
We explicitly construct a coupling attaining Ornstein's -distance
between ordered pairs of binary chains of infinite order. Our main tool is a
representation of the transition probabilities of the coupled bivariate chain
of infinite order as a countable mixture of Markov transition probabilities of
increasing order. Under suitable conditions on the loss of memory of the
chains, this representation implies that the coupled chain can be represented
as a concatenation of iid sequence of bivariate finite random strings of
symbols. The perfect simulation algorithm is based on the fact that we can
identify the first regeneration point to the left of the origin almost surely.Comment: Typos corrected. The final publication is available at
http://www.springerlink.co
Perfect simulation of spatial processes
This work presents a review of some of the schemes used to perfect sample from spatial processes
Continuity properties of a factor of Markov chains
Starting from a Markov chain with a finite alphabet, we consider the chain
obtained when all but one symbol are undistinguishable for the practitioner. We
study necessary and sufficient conditions for this chain to have continuous
transition probabilities with respect to the past
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