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Integration with respect to fractal functions and stochastic calculus. II. (English) Zbl 0983.60054
The author continues to study the link between fractional and stochastic calculus established in part I [Probab. Theory Relat. Fields 111, No. 3, 333-374 (1998; Zbl 0918.60037)]. A fractional integral operator extending the Lebesgue-Stieltjes integral is studied and a related concept of stochastic integral which is similar to the so-called forward integral in stochastic integration theory is introduced. The results are applied to ordinary differential equations driven by fractal functions and to anticipative stochastic differential equations whose noise processes possess absolutely continuous generalized covariation processes.

MSC:
60H05 Stochastic integrals
26A42 Integrals of Riemann, Stieltjes and Lebesgue type
26A33 Fractional derivatives and integrals
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