Dilatively semistable stochastic processes

Peter Kern; Lina Wedrich

doi:10.1016/j.spl.2015.01.008

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arXiv · 1410.2727

Dilatively semistable stochastic processes

Peter Kern·Lina Wedrich

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Abstract

Dilative semistability extends the notion of semi-selfsimilarity for infinitely divisible stochastic processes by introducing an additional scaling in the convolution exponent. It is shown that this scaling relation is a natural extension of dilative stability and some examples of dilatively semistable processes are given. We further characterize dilatively stable and dilatively semistable processes as limits for certain rescaled aggregations of independent processes.

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Peter Kern, Lina Wedrich. 2014-10-10. Dilatively semistable stochastic processes. https://doi.org/10.1016/j.spl.2015.01.008

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