Integration with respect to Fractal Functions and Stochastic Calculus II

Abstract

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 [21].