SECOND-ORDER ASYMPTOTIC EXPANSION FOR THE ESTIMATOR
OF THE COVARIANCE OF TWO ASYNCHRONOUSLY OBSERVED
DIFFUSION PROCESSES


Arnak DALALYAN
Univerité Pierre et Marie Curie
France

Nakahiro YOSHIDA
Tokyo University
Japan


ABSTRACT

We consider the problem of estimating the covariance of two one-dimensional diffusion processes. We assume that these processes are observed discretely and but the observation times of two processes may differ. We obtain an asymptotic second-order expansion for the law of the quasi-maximum likelihood estimator when the frequency of observation for both processes tends to zero. We discuss in more detail the case where the observation times are independent Poisson point processes independent of underlying diffusion processes.



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