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Article Dans Une Revue Rocky Mountain Journal of Mathematics Année : 2006

From N parameter fractional Brownian motions to N parameter multifractional Brownian motions

Résumé

Multifractional Brownian motion is an extension of the well-known fractional Brownian motion where the H¨older regularity is allowed to vary along the paths. In this paper, two kinds of multi-parameter extensions of mBm are studied: one is isotropic while the other is not. For each of these processes, a moving average representation, a harmonizable representation, and the covariance structure are given. The H¨older regularity is then studied. In particular, the case of an irregular exponent function H is investigated. In this situation, the almost sure pointwise and local Holder exponents of the multi-parameter mBm are proved to be equal to the correspondent exponents of H. Eventually, a local asymptotic self-similarity property is proved. The limit process can be another process than fBm.
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Dates et versions

hal-00539236 , version 1 (24-01-2011)

Identifiants

  • HAL Id : hal-00539236 , version 1

Citer

Erick Herbin. From N parameter fractional Brownian motions to N parameter multifractional Brownian motions. Rocky Mountain Journal of Mathematics, 2006, 36 (4), pp.1249-1284. ⟨hal-00539236⟩
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