From N parameter fractional Brownian motions to N parameter multifractional Brownian motions
By Érick Herbin. 2005
91 citations recorded by the source corpus.
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.
Subfields: Economics and Econometrics, Finance
View Paper: https://www.semanticscholar.org/paper/962d03e3db923332743f7a7044c520284d61c8ac
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Economics and Econometrics
- Hans-Peter Scheffler
- Donald B. Percival
- Mark M. Meerschaert
- Hana vSevvc'ikov'a
- Tilmann Gneiting
- Hermine Bierm'e
- Yimin Xiao
- Dongsheng Wu
In Finance
- Dongsheng Wu
- Yimin Xiao
- Hermine Bierm'e
- Donald B. Percival
- Mark M. Meerschaert
- Hana vSevvc'ikov'a
- Hans-Peter Scheffler
- Tilmann Gneiting
Citations in the corpus
- Operator scaling stable random fields (2006, background): “See [5,13,21] and the literature cited there for more information on these fields.”
- Geometric Properties of Fractional Brownian Sheets (2007, methodology): “While the argument of Khoshnevisan and Xiao [29] relies on the property of independent increments of the Brownian sheet, our proof is based on a Fourier analytic argument in Kahane ([22], Chapter 18) and the following harmonizable representation of BH 0 essentially due to Herbin [20]: B 0 (t) = K −1”
- Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data (2011, background): “Multifractional Brownian motion (Peltier and Levy Vehel, 1995; Benassi, Jaffard and Roux, 1997; Herbin, 2006) is a generalization of the classical fractional Brownian motion, where the fractal dimension is allowed to vary along the sample paths.”