✦ LIBER ✦

Integration with respect to Fractal Functions and Stochastic Calculus II

✍ Scribed by M. Zähle

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 371 KB
Volume: 225
Category: Article
ISSN: 0025-584X
DOI: 10.1002/1522-2616(200105)225:1<145::aid-mana145>3.0.co;2-0

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✦ Synopsis

The link between fractional and stochastic calculus established in part I of this paper is investigated in more detail. We study a fractional integral operator extending the Lebesgue-Stieltjes integral and introduce a related concept of stochastic integral which is similar to the so -called forward integral in stochastic integration theory. The results are applied to ODE driven by fractal functions and to anticipative SDE whose noise processes possess absolutely continuous generalized covariation processes. A survey on this approach may be found in .

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