Parametric Estimation of Diffusion Processes Sampled at First Exit Times

Details Parametric Estimation of Diffusion Processes Sampled at First Exit Times Parametric Estimation of Diffusion Processes Sampled at First Exit Times

2003-05-19

arxiv.org/abs/math/0305273v2

International Journal of Pure and Applied Mathematics, 7, No. 4 (2003), 449-486. MR1994830 (2004c:62175)

Mathematics

Statistics Theory

31 pages, http://math.ucr.edu/~jlondono

Scientific paper

This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and asymptotic normality of an appropriate normalization are proved. The results are applied to two examples from the financial literature; viz., Cox-Ingersoll-Ross' model and the constant elasticity of variance (CEV) process illustrate the use of the technique proposed herein.

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