OF THE COVARIANCE OF TWO ASYNCHRONOUSLY OBSERVED

DIFFUSION PROCESSES

Univerité Pierre et Marie Curie

France

Tokyo University

Japan

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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