| Título: | The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6 |
| Autores: |
Nourdin, Ivan; Université Nancy 1 Réveillac, Anthony; Humboldt-University Swanson, Jason; University of Central Florida |
| Fecha: | 2010-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Stochastic integration; Stratonovich integral; fractional Brownian motion; weak convergence; Malliavin calculus 60H05; 60G15; 60G18; 60J05. |
| Descripción: | Let $B$ be a fractional Brownian motion with Hurst parameter $H=1/6$. It is known that the symmetric Stratonovich-style Riemann sums for $\int\!g(B(s))\,dB(s)$ do not, in general, converge in probability. We show, however, that they do converge in law in the Skorohod space of càdlàg functions. Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correction term that is an ordinary Itô integral with respect to a Brownian motion that is independent of $B$. |
| Idioma: | No aplica |
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