Article2006

Some properties of the sub-fractional Brownian motion

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Stochastic processes and financial applications Stochastic processes and statistical mechanics Fractional Differential Equations Solutions

Abstract

We study several properties of the sub-fractional Brownian motion (fBm) introduced by Bojdecki et al. related to those of the fBm. This process is a self-similar Gaussian process depending on a parameter H ∈ (0, 2) with non stationary increments and is a generalization of the Brownian motion (Bm). The strong variation of the indefinite stochastic integral with respect to sub-fBm is also discussed.

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References

1968Fractional Brownian Motions, Fractional Noises and Applications 1998Integration with respect to fractal functions and stochastic calculus. I 2001Mixed Fractional Brownian Motion 2004A series expansion of fractional Brownian motion 2005On bifractional Brownian motion 2000Stochastic calculus with respect to continuous finite quadratic variation processes

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