ISSN:
1572-9311
Keywords:
ergodic diffusions
;
local time
;
empirical density
;
uniform convergence
;
density estimation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We investigate the uniform convergence of the density of the empirical measure of an ergodic diffusion. It is known that under certain conditions on the drift and diffusion coefficients of the diffusion, the empirical density f t converges in probability to the invariant density f, uniformly on the entire real line. We show that under the same conditions, uniform convergence of f t to f on compact intervals takes place almost surely. Moreover, we prove that under much milder conditions (the usual linear growth condition on the drift and diffusion coefficients and a finite second moment of the invariant measure suffice), we have the uniform convergence of f t to f on compacta in probability.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1009949802518
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