Integration with respect to Fractal Functions and Stochastic Calculus II

The link between fractional and stochastic calculus established in part I o f 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 i ntegral in stochastic integration theory. The results are applied to ODE dr iven by fractal functions and to anticipative SDE whose noise processes pos sess absolutely continuous generalized covariation processes. h survey on t his approach may be found in [21].