Asymptotic normality for discretely observed Markov jump processes with an absorbing state

For a continuous-time Markov process, occasionally, only discrete-time observations are available. For a simple sample of homogeneous Markov jump processes with an absorbing state, observed each on a stochastic grid of time points, we establish asymptotic normality of the maximum likelihood estimato...

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Bibliographic Details
Published in:Statistics & probability letters 2014-07, Vol.90, p.136-139
Main Authors: Kremer, Alexander, Weißbach, Rafael
Format: Article
Language:English
Subjects:
Asymptotic normality
Discrete observations
Multiple Markov jump process
Parametric maximum likelihood
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Summary:For a continuous-time Markov process, occasionally, only discrete-time observations are available. For a simple sample of homogeneous Markov jump processes with an absorbing state, observed each on a stochastic grid of time points, we establish asymptotic normality of the maximum likelihood estimator and close the gap in Kremer and Weißbach (2013). By showing that the solution of the Kolmogorov backward equation system is continuous differentiable, we can apply results for M-estimators.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2014.03.010