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A class of micropulses and antipersistent fractional Brownian motion. (English) Zbl 0846.60055
Summary: We begin with stochastic processes obtained as sums of “up-and-down” pulses with random moments of birth $$\tau$$ and random lifetime $$w$$ determined by a Poisson random measure. When the pulse amplitude $$\varepsilon \to 0$$, while the pulse density $$\delta$$ increases to infinity, one obtains a process of “fractal sum of micropulses.” A CLT style argument shows convergence in the sense of finite-dimensional distributions to a Gaussian process with negatively correlated increments. In the most interesting case the limit is fractional Brownian motion (FBM), a self-affine process with the scaling constant $$0 < H < 1/2$$. The construction is extended to the multidimensional FBM field as well as to micropulses of more complicated shape.

##### MSC:
 60G99 Stochastic processes 60J65 Brownian motion
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##### References:
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