Article2001

Integration with respect to Fractal Functions and Stochastic Calculus II

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Stochastic processes and financial applications Fractional Differential Equations Solutions Fuzzy Systems and Optimization

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].

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References

1968Fractional Brownian Motions, Fractional Noises and Applications 1983Stochastic Differential Equations and Diffusion Processes 2006The Malliavin Calculus and Related Topics 1998Differential equations driven by rough signals 1951Multiple Wiener Integral 1998Integration with respect to fractal functions and stochastic calculus. I 1988Stochastic calculus with anticipating integrands 1978On the Gap Between Deterministic and Stochastic Ordinary Differential Equations

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