Title

The Calculus Of Differentials For The Weak Stratonovich Integral

Keywords

Fractional Brownian motion; Stochastic integration; Stratonovich integral; Weak convergence

Abstract

The weak Stratonovich integral is defined as the limit, in law, of Stratonovich-type symmetric Riemann sums. We derive an explicit expression for the weak Stratonovich integral of f(B) with respect to g(B), where B is a fractional Brownian motion with Hurst parameter 1/6, and f and g are smooth functions. We use this expression to derive an Itô-type formula for this integral. As in the case where g is the identity, the Itô-type formula has a correction term which is a classical Itô integral and which is related to the so-called signed cubic variation of g(B). Finally, we derive a surprising formula for calculating with differentials. We show that if dM = X dN, then Z dM can be written as ZX dN minus a stochastic correction term which is again related to the signed cubic variation. © Springer Science+Business Media New York 2013.

Publication Date

1-1-2013

Publication Title

Springer Proceedings in Mathematics and Statistics

Volume

34

Number of Pages

95-111

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/978-1-4614-5906-4_5

Socpus ID

84883425057 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84883425057

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