Displaying similar documents to “Chaos expansions and local times.”

On the Karhunen-Loeve expansion for transformed processes.

Ramón Gutiérrez Jáimez, Mariano J. Valderrama Bonnet (1987)

Trabajos de Estadística

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We discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.

Multivariate normal approximation using Stein’s method and Malliavin calculus

Ivan Nourdin, Giovanni Peccati, Anthony Réveillac (2010)

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

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We combine Stein’s method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of gaussian fields. Among several examples, we provide an application to a functional version of the Breuer–Major CLT for fields subordinated to a fractional brownian motion.

Multiparameter multifractional brownian motion : local nondeterminism and joint continuity of the local times

Antoine Ayache, Narn-Rueih Shieh, Yimin Xiao (2011)

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

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By using a wavelet method we prove that the harmonisable-type -parameter multifractional brownian motion (mfBm) is a locally nondeterministic gaussian random field. This nice property then allows us to establish joint continuity of the local times of an (, )-mfBm and to obtain some new results concerning its sample path behavior.