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June 2006 Parametric inference for discretely observed non-ergodic diffusions
Jean Jacod
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Bernoulli 12(3): 383-401 (June 2006). DOI: 10.3150/bj/1151525127


We consider a multidimensional diffusion process X whose drift and diffusion coefficients depend respectively on a parameter λ and θ. This process is observed at n+1 equally spaced times 0,Δn,2Δn,,nΔn, and Tn=nΔn denotes the length of the `observation window'. We are interested in estimating λ and/or θ. Under suitable smoothness and identifiability conditions, we exhibit estimators λ̂n and θ̂n, such that the variables n.(θ̂n-θ) and Tn(λ̂n-λ) are tight for Δn0 and Tn. When λ is known, we can even drop the assumption that Tn. These results hold without any kind of ergodicity or even recurrence assumption on the diffusion process.


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Jean Jacod. "Parametric inference for discretely observed non-ergodic diffusions." Bernoulli 12 (3) 383 - 401, June 2006.


Published: June 2006
First available in Project Euclid: 28 June 2006

zbMATH: 1100.62081
MathSciNet: MR2232724
Digital Object Identifier: 10.3150/bj/1151525127

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability


Vol.12 • No. 3 • June 2006
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