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On the First-Order Edgeworth Expansion for a Markov Chain

✍ Scribed by S. Datta; W.P. Mccormick

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
474 KB
Volume
44
Category
Article
ISSN
0047-259X

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✦ Synopsis

We consider the first-order Edgeworth expansion for summands related to a homogeneous Markov chain. Certain inaccuracies in some earlier results by Nagaev are corrected and the expansion is obtained under relaxed conditions. An application of our result to the distribution of the mle of a transition probability in the countable state space case is also considered.

1993 Academic Press. Inc.

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## Abstract First‐order phase transitions are modelled by a non‐homogeneous, time‐dependent scalar‐valued order parameter or phase field. The time dependence of the order parameter is viewed as arising from a balance law of the structure order. The gross motion is disregarded and hence the body is