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Estimation of an Ergodic Diffusion from Discrete Observations
Author(s) -
Kessler Mathieu
Publication year - 1997
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00059
Subject(s) - mathematics , ergodic theory , equidistant , diffusion process , estimator , diffusion , discretization , integer (computer science) , combinatorics , mathematical analysis , statistics , geometry , physics , thermodynamics , knowledge management , innovation diffusion , computer science , programming language
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 n i = ih n , 1 ≤ i ≤ n . We assume that h n ← 0 and nh n ←∞. Under the condition nh n p ← 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).