Title

The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6

Authors

Authors

I. Nourdin; A. Reveillac;J. Swanson

Comments

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Abbreviated Journal Title

Electron. J. Probab.

Keywords

Stochastic integration; Stratonovich integral; fractional Brownian; motion; weak convergence; Malliavin calculus; WEIGHTED QUADRATIC VARIATIONS; LIMIT-THEOREMS; CALCULUS; FORMULA; Statistics & Probability

Abstract

Let B be a fractional Brownian motion with Hurst parameter H = 1 = 6. It is known that the symmetric Stratonovich-style Riemann sums for integral g (B(s)) dB (s) do not, in general, converge in probability. We show, however, that they do converge in law in the Skorohod space of cadlag functions. Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correction term that is an ordinary It integral with respect to a Brownian motion that is independent of B.

Journal Title

Electronic Journal of Probability

Volume

15

Publication Date

1-1-2010

Document Type

Article

Language

English

First Page

2117

Last Page

2162

WOS Identifier

WOS:000285654000001

ISSN

1083-6489

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