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ON LIKELIHOOD ESTIMATION FOR DISCRETELY OBSERVED MARKOV JUMP PROCESSES
Author(s) -
Dehay Dominique,
Yao JianFeng
Publication year - 2007
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2006.00466.x
Subject(s) - mathematics , likelihood function , ergodicity , jump , estimator , consistency (knowledge bases) , markov chain , jump process , markov process , maximum likelihood , asymptotic distribution , jump diffusion , statistics , discrete mathematics , physics , quantum mechanics
Summary The parameter estimation problem for a Markov jump process sampled at equidistant time points is considered here. Unlike the diffusion case where a closed form of the likelihood function is usually unavailable, here an explicit expansion of the likelihood function of the sampled chain is provided. Under suitable ergodicity conditions on the jump process, the consistency and the asymptotic normality of the likelihood estimator are established as the observation period tends to infinity. Simulation experiments are conducted to demonstrate the computational facility of the method.