Source: Adv. in Appl. Probab.
Volume 43, Number 3
We present a new perfect simulation algorithm for stationary chains having
unbounded variable length memory. This is the class of infinite memory chains
for which the family of transition probabilities is represented by a
probabilistic context tree. We do not assume any continuity condition:
our condition is expressed in terms of the structure of the context tree. More
precisely, the length of the contexts is a deterministic function of the
distance to the last occurrence of some determined string of symbols. It turns
out that the resulting class of chains can be seen as a natural extension of
the class of chains having a renewal string. In particular, our chains exhibit
a visible regeneration scheme.
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