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Estimation of the Diffusion Coefficient from Crossings

Florens, Danielle (1999), Estimation of the Diffusion Coefficient from Crossings, Statistical Inference for Stochastic Processes, 1, 2, p. 175-195. http://dx.doi.org/10.1023/A:1009927813898

Type
Article accepté pour publication ou publié
Date
1999
Journal name
Statistical Inference for Stochastic Processes
Volume
1
Number
2
Publisher
Springer
Pages
175-195
Publication identifier
Metadata
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Author(s)
Florens, Danielle
Abstract (EN)
In a previous work we proposed a kernel method for estimating the value of a state‐dependent diffusion coefficient σ(x) from discrete time observations. We propose an estimator of the value σ(x), based on the squared length of the transitions where a crossing past the level x takes place and we investigate its limit properties. Using the Poisson equation and other limit theorems for discrete martingales, we prove consistency and asymptotic mixed normality of this estimator.
Subjects / Keywords
diffusions; local time; crossings; discretization