From N-parameter fractional Brownian motions to N-parameter multifractional Brownian motions
| dc.creator | Herbin, E. | |
| dc.date | 2005-03-09 | |
| dc.date.accessioned | 2026-07-07T05:17:50Z | |
| dc.date.available | 2026-07-07T05:17:50Z | |
| dc.description | Multifractional Brownian motion is an extension of the well-known fractional Brownian motion where the Holder regularity is allowed to vary along the paths. In this paper, two kind 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 Holder 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. | |
| dc.description | 36 pages | |
| dc.identifier | https://arxiv.org/abs/math/0503182 | |
| dc.identifier | http://arxiv.org/abs/math/0503182 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74449 | |
| dc.subject | Probability | |
| dc.subject | 62G05; 60G15; 60G17; 60G18 | |
| dc.title | From N-parameter fractional Brownian motions to N-parameter multifractional Brownian motions | |
| dc.type | text |