Bernoulli

  • Bernoulli
  • Volume 12, Number 3 (2006), 383-401.

Parametric inference for discretely observed non-ergodic diffusions

Jean Jacod

Full-text: Open access

Abstract

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 ,Δ n,2Δ n,,nΔ n , and T n =nΔ n 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 λ ̂ n and θ ̂ n , such that the variables n .(θ ̂ n-θ) and T n (λ ̂ n-λ) are tight for Δ n 0 and T n . When λ is known, we can even drop the assumption that T n . These results hold without any kind of ergodicity or even recurrence assumption on the diffusion process.

Article information

Source
Bernoulli, Volume 12, Number 3 (2006), 383-401.

Dates
First available in Project Euclid: 28 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1151525127

Digital Object Identifier
doi:10.3150/bj/1151525127

Mathematical Reviews number (MathSciNet)
MR2232724

Zentralblatt MATH identifier
1100.62081

Keywords
non-ergodic diffusion processes parametric inference for diffusions

Citation

Jacod, Jean. Parametric inference for discretely observed non-ergodic diffusions. Bernoulli 12 (2006), no. 3, 383--401. doi:10.3150/bj/1151525127. https://projecteuclid.org/euclid.bj/1151525127


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