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February 1997 A central limit theorem for normalized functions of the increments of a diffusion process, in the presence of round-off errors
Sylvain Delattre, Jean Jacod
Bernoulli 3(1): 1-28 (February 1997).

Abstract

Let X be a one-dimensional diffusion process. For each n 1 we have a round-off level α n >0 and we consider the rounded-off value X t ( α) =α[X t/α] . We are interested in the asymptotic behaviour of the processes U (n,φ) t=1 n 1 i[nt]φ(X ( i-1)/n ( α),n (X i /n ( α)-X ( i-1)/n ( α))) as n goes to + : under suitable assumptions on φ , and when the sequence α n goes to a limit β [0,) , we prove the convergence of U (n,φ) to a limiting process in probability (for the local uniform topology), and an associated central limit theorem. This is motivated mainly by statistical problems in which one wishes to estimate a parameter occurring in the diffusion coefficient, when the diffusion process is observed at times i /n and is subject to rounding off at some level α n which is 'small' but not 'very small'.

Citation

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Sylvain Delattre. Jean Jacod. "A central limit theorem for normalized functions of the increments of a diffusion process, in the presence of round-off errors." Bernoulli 3 (1) 1 - 28, February 1997.

Information

Published: February 1997
First available in Project Euclid: 4 May 2007

zbMATH: 0882.60017
MathSciNet: MR1466543

Keywords: Functional limit theorems , round-off errors

Rights: Copyright © 1997 Bernoulli Society for Mathematical Statistics and Probability

Vol.3 • No. 1 • February 1997
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