2008 | OriginalPaper | Buchkapitel
Fractional Wick Itô Skorohod (fWIS) integrals for fBm of Hurst index H >1/2
Erschienen in: Stochastic Calculus for Fractional Brownian Motion and Applications
Verlag: Springer London
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In this chapter we introduce the definition of stochastic integral with respect to the
fBm
for Hurst index 1
/
2
<H <
1 by using the white noise analysis method. At this purpose we define the
fractional white noise
and stochastic integral as an element in the
fractional Hida distribution space
.
To obtain a classical Itô formula, we need the stochastic integral to be an ordinary random variable. Hence the
ø
-derivative is introduced to handle the existence of the Wick product in
L
2
. Classical Itô type formulas are obtained and applications are discussed. The main references for this chapter are [32], [83] and [121].