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# Estimation of an Ergodic Diffusion from Discrete Observations

Mathieu Kessler
Scandinavian Journal of Statistics
Vol. 24, No. 2 (Jun., 1997), pp. 211-229
Stable URL: http://www.jstor.org/stable/4616449
Page Count: 19
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## 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 $t_{i}^{n}=ih_{n}$, 1 ≤ i ≤ n. We assume that hn→ 0 and $nh_{n}\rightarrow \infty$. Under the condition $nh_{n}^{p}\rightarrow 0$ 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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