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| HAL: hal-00653808, version 4 |
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| Available versions | v1 (2011-12-20) | v2 (2012-04-19) | v3 (2012-07-14) | v4 (2012-07-16) | v5 (2012-11-27) |
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| Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motions |
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| Erick Herbin 1, 2Joachim Lebovits 1, 3 |
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| (2011-12-20) |
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| 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. |
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| 1: | REGULARITY (INRIA Saclay - Ile de France) |
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INRIA – Ecole Centrale Paris |
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| 2: | Mathématiques Appliquées aux Systèmes - EA 4037 (MAS) |
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Ecole Centrale Paris |
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| 3: | Laboratoire de Probabilités et Modèles Aléatoires (LPMA) |
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CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot |
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| Domain | : | Mathematics/Probability |
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| Attached file list to this document: | |||||
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| hal-00653808, version 4 | |
| http://hal.inria.fr/hal-00653808 | |
| oai:hal.inria.fr:hal-00653808 | |
| From: Joachim Lebovits | |
| Submitted on: Monday, 16 July 2012 10:13:34 | |
| Updated on: Monday, 16 July 2012 13:44:57 | |
