230 research outputs found
Hsu-Robbins and Spitzer's theorems for the variations of fractional Brownian motion
Using recent results on the behavior of multiple Wiener-It\^o integrals based
on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of
correlated random variables related to the increments of the fractional
Brownian motion.Comment: To appear in "Electronic Communications in Probability
Limits of bifractional Brownian noises
Let be a bifractional Brownian motion with
two parameters and . The main result of this paper is
that the increment process generated by the bifractional Brownian motion
converges when to
, where is the
fractional Brownian motion with Hurst index . We also study the behavior of
the noise associated to the bifractional Brownian motion and limit theorems to
Variations and estimators for the selfsimilarity order through Malliavin calculus
Using multiple stochastic integrals and the Malliavin calculus, we analyze
the asymptotic behavior of quadratic variations for a specific non-Gaussian
self-similar process, the Rosenblatt process. We apply our results to the
design of strongly consistent statistical estimators for the self-similarity
parameter . Although, in the case of the Rosenblatt process, our estimator
has non-Gaussian asymptotics for all , we show the remarkable fact that
the process's data at time 1 can be used to construct a distinct, compensated
estimator with Gaussian asymptotics for
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