Estimation of an Ergodic Diffusion from Discrete Observations

Abstract

We consider a one‐dimensional diffusion process X, with ergodic property, with drift b(x, θ) and diffusion coefficient a(x, σ) depending on unknown parameters θ and σ. We are interested in the joint estimation of (θ, σ). For that purpose, we dispose of a discretized trajectory, observed at n equidistant times tni = ihn, 1 ≤i≤n. We assume that hn← 0 and nhn←∞. Under the condition nhnp← 0 for an arbitrary integer p, we exhibit a contrast dependent on p which provides us with an asymptotically normal and efficient estimator of (θ, σ).

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