Article Dans Une Revue ALEA : Latin American Journal of Probability and Mathematical Statistics Année : 2018

Almost sure approximations in Hölder norms of a general stochastic process defined by a Young integral

Céline Esser
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Qidi Peng
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Résumé

We focus on a stochastic process {Y (t)} t∈[0,v] defined by a pathwise Young integral of a general form. Thanks to the Haar basis, we connect the classical method of approximation of {Y (t)} t∈[0,v] through Euler scheme and Riemann-Stieltjes sums with a new approach consisting in the use of an appropriate series representation of {Y (t)} t∈[0,v]. This representation is obtained through a general compactly supported orthonormal wavelet basis. An advantage offered by the new approach with respect to the classical one is that a better almost sure rate of convergence in Hölder norms can be derived, under a general Wiener chaos condition. Also, this improved rate turns out to be optimal in some situations; typically, when the integrand and integrator associated to {Y (t)} t∈[0,v] are independent fractional Brownian motions with appropriate Hurst parameters.

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hal-04333428 , version 1 (09-12-2023)

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  • HAL Id : hal-04333428 , version 1

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Antoine Ayache, Céline Esser, Qidi Peng. Almost sure approximations in Hölder norms of a general stochastic process defined by a Young integral. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2018, 15. ⟨hal-04333428⟩
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