Fractal Process

A 1-D Map whose increments are distributed according to a Normal Distribution. Let $y(t-\Delta t)$ and $y(t+\Delta t)$ be values, then their correlation is given by the Brown Function

$$r=2^{2H-1}-1.$$

When $H=1/2$, $r=0$ and the fractal process corresponds to 1-D Brownian motion. If $H>1/2$, then $r>0$ and the process is called a Persistent Process. If $H<1/2$, then $r<0$ and the process is called an Antipersistent Process.

See also Antipersistent Process, Persistent Process

References

von Seggern, D. CRC Standard Curves and Surfaces. Boca Raton, FL: CRC Press, 1993.