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Le Guével, R.; Véhel, J. Lévy

A Ferguson-Klass-LePage series representation of multistable multifractional motions and related processes. (English) Zbl 1260.60096

Bernoulli 18, No. 4, 1099-1127 (2012).
Summary: The study of non-stationary processes whose local form has controlled properties is a fruitful and important area of research, both in theory and application. In [K.J. Falconer and the second author, J. Theor. Probab. 22, No. 2, 375–401 (2009; Zbl 1171.60010)], a particular way of constructing such processes was investigated, leading in particular to multifractional multistable processes, which were built using sums over Poisson processes. We present here a different construction of these processes, based on the Ferguson-Klass-LePage series representation of stable processes. We consider various particular cases of interest, including multistable Lévy motion, multistable reverse Ornstein-Uhlenbeck process, log-fractional multistable motion and linear multistable multifractional motion. We also show that the processes defined here have the same finite dimensional distributions as the corresponding processes built in [loc. cit.]. Finally, we display numerical experiments showing graphs of synthesized paths of such processes.

Cited in 1 Review
Cited in 15 Documents

MSC:

60G52 Stable stochastic processes
60G17 Sample path properties

Keywords:

Ferguson-Klass-LePage series representation; localisable processes; multifractional processes; stable processes

Citations:

Zbl 1171.60010
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Full Text: DOI arXiv Euclid

References:

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