ALTERNATIVE MICROPULSES AND FRACTIONAL BROWNIAN-MOTION

We showed in an earlier paper (1995a) that negatively correlated fract ional Brownian motion (FBM) can be generated as a fractal sum of one k ind of micropulses (FSM). That is, FBM of exponent H < 1/2 is the limi t (in the sense of finite-dimensional distributions) of a certain sequ ence of processes obtained as sums of rectangular pulses. We now show that more general pulses yield a wide range of FBMs: either negatively (as before) or positively (H > 1/2) correlated. We begin with triangu lar (conical and semi-conical) pulses. To transform them into micropul ses, the base angle is made to decrease to zero, while the number of p ulses, determined by a Poisson random measure, is made to increase to infinity. Then we extend our results to more general pulse shapes.