**Les Cahiers de Recherche - HEC Paris**
# No 756:

Approximating a sequence of observations by a simple process

*Nicolas VIEILLE, Dinah ROSENBERG *()

* and Eilon SOLAN *()

**Abstract:** Given a sequence (s0; s1,..., sN) of observations from a
finite set S, we construct a process (sn)n_<N that satisfies the following
properties: (i) (Sn)n_< ·N is a piecewise Markov chain, (ii) the
conditional distribution of sn given S0,...,Sn-1 is close to the empirical
transition given by the observed sequence, for most n's, (iii) under
(Sn)n_<N, with high probability the empirical frequency of the realized
sequence is close to the one given by the observed sequence. We generalize
this result to the case that the conditional distribution of Sn given
S0,...,Sn-1 is required to be in some polyhedron Vs n-1.

**Keywords:** Markov chains; approximation theory; (follow links to similar papers)

**JEL-Codes:** C40; C44; (follow links to similar papers)

29 pages, April 24, 2002

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