- Volume 3, Number 1 (1997), 1-28.
A central limit theorem for normalized functions of the increments of a diffusion process, in the presence of round-off errors
Let be a one-dimensional diffusion process. For each we have a round-off level and we consider the rounded-off value . We are interested in the asymptotic behaviour of the processes as goes to : under suitable assumptions on , and when the sequence goes to a limit , we prove the convergence of 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 and is subject to rounding off at some level which is 'small' but not 'very small'.
Bernoulli, Volume 3, Number 1 (1997), 1-28.
First available in Project Euclid: 4 May 2007
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Delattre, Sylvain; Jacod, Jean. A central limit theorem for normalized functions of the increments of a diffusion process, in the presence of round-off errors. Bernoulli 3 (1997), no. 1, 1--28. https://projecteuclid.org/euclid.bj/1178291930