Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motions

Abstract : Stochastic integration w.r.t. fractional Brownian motion (fBm) has raised strong interest in recent years, motivated in particular by applications in finance and Internet traffic modelling. Since fBm is not a semi-martingale, stochastic integration requires specific developments. Multifractional Brownian motion (mBm) generalizes fBm by letting the local Hölder exponent vary in time. This is useful in various areas, including financial modelling and biomedicine. The aim of this work is twofold: first, we prove that an mBm may be approximated in law by a sequence of "tangent" fBms. Second, using this approximation, we show how to construct stochastic integrals w.r.t. mBm by "transporting" corresponding integrals w.r.t. fBm. We illustrate our method on examples such as the Hitsuda-Skohorod and Wick-Itô stochastic integrals.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal.inria.fr/hal-00653808
Contributor : Joachim Lebovits <>
Submitted on : Monday, November 26, 2012 - 6:18:50 PM
Last modification on : Friday, July 26, 2019 - 2:14:27 PM
Long-term archiving on : Saturday, December 17, 2016 - 3:54:35 PM

File

Stochastic_Calculus_wrt_MBM_vi...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00653808, version 5

Citation

Erick Herbin, Joachim Lebovits, Jacques Lévy Véhel. Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motions. 2012. ⟨hal-00653808v5⟩

Share

Metrics

Record views

99

Files downloads

127