Fractional Brownian Motion

Click the picture to animate.

Here is a graph of fBm with H = 1/2.

From this H, the expected value of the product of the increments is zero, so Y(t) - Y(0) and Y(t + h) - Y(t) are as likely to have the same signs as to have opposite signs.

In fact, the increments are independent, and index H = 1/2 fBm is just standard Brownian motion.

Click on the picture to see the corresponding picture with 1, 2, 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50 terms.

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