DOIAbstract
AbstractA self-similar process Z(t) has stationary increments and is invariant in law under the transformation Z(i)→c-HZ(ct), c⩾0. The choice 12<H<1 ensures that the increments of Z(t) exhibit a long range positive correlation.Mandelbrot and Van Ness investigated the case where Z(t) is Gaussian and represented that Gaussian self-similar process as a fractional integral of Brownian motion. They called it fractional Brownian motion. This paper provides a time-indexed representation for a sequence of self- similar processes Z̄m(t), m=1,2,…, whose finite-dimensional moments have been specified in an earlier paper. Z̄1(t) is the Gaussian fractional Brownian motion but the processZ̄m(t) are not Gaussian when m⩾2.Self-similar processes are being s...
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