Article2015

Derivative for self-intersection local time of multidimensional fractional Brownian motion

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Stochastic processes and financial applications Stochastic processes and statistical mechanics Fractional Differential Equations Solutions

Abstract

Let be a fractional Brownian motion taking values in with Hurst index . In this paper, we consider the self-intersection local time and its derivative in the spatial variable . In particular, we introduce the so-called integrated quadratic covariation and show that the Bouleau-Yor type identityholds for some suitable .

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References

2008Stochastic Calculus for Fractional Brownian Motion and Related Processes 2007A Change-of-Variable Formula with Local Time on Surfaces 2005Integral transformations and anticipative calculus for fractional Brownian motions 2005A Change-of-Variable Formula with Local Time on Curves 2005Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H∈(0,12)2004m-order integrals and generalized Itô's formula; the case of a fractional Brownian motion with any Hurst index 2000Integration with respect to local time 2003Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index ${H \ge \frac{1}{4}}$

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