Anzeige
Erschienen in:
2013 | OriginalPaper | Buchkapitel
5. The Calculus of Differentials for the Weak Stratonovich Integral
verfasst von : Jason Swanson
Erschienen in: Malliavin Calculus and Stochastic Analysis
Verlag: Springer US
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
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 d
M = X
d
N, then Z
d
M can be written as ZX
d
N minus a stochastic correction term which is again related to the signed cubic variation.