Convergence and convergence rate to fractional Brownian motion for weighted random sums.

Konstantopoulos, Takis; Sakhanenko, A.I.

Displaying similar documents to “Convergence and convergence rate to fractional Brownian motion for weighted random sums.”

Hsu-Robbins and Spitzer's theorems for the variations of fractional Brownian motion.

Tudor, Ciprian A. (2009)

Electronic Communications in Probability [electronic only]

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Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion.

Breton, Jean-Christophe, Nourdin, Ivan (2008)

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Approximation of the fractional Brownian sheet Ornstein-Uhlenbeck sheet

Laure Coutin, Monique Pontier (2007)

ESAIM: Probability and Statistics

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A stochastic “Fubini” lemma and an approximation theorem for integrals on the plane are used to produce a simulation algorithm for an anisotropic fractional Brownian sheet. The convergence rate is given. These results are valuable for any value of the Hurst parameters $(α_{1}, α_{2}) \in {] 0, 1 [}^{2}, α_{i} \neq \frac{1}{2} .$ Finally, the approximation process is iterative on the quarter plane $ℝ_{+}^{2} .$ A sample of such simulations can be used to test estimators of the parameters = 1,2.

Self-similar processes in collective risk theory.

Michna, Zbigniew (1998)

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Invariance principle, multifractional gaussian processes and long-range dependence

Serge Cohen, Renaud Marty (2008)

Annales de l'I.H.P. Probabilités et statistiques

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This paper is devoted to establish an invariance principle where the limit process is a multifractional gaussian process with a multifractional function which takes its values in (1/2, 1). Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional brownian motion.