Some Singular Sample Path Properties of a Multiparameter Fractional Brownian Motion

Alexandre Richard ()
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Alexandre Richard: École Centrale Paris-INRIA Regularity Team

Journal of Theoretical Probability, 2017, vol. 30, issue 4, 1285-1309

Abstract: Abstract We obtain a spectral representation and compute the small ball probabilities for a (non-increment stationary) multiparameter extension of the fractional Brownian motion. We derive from these results a Chung-type law of the iterated logarithm at the origin and exhibit the singular behaviour of this multiparameter fractional Brownian motion, as it behaves very differently at the origin and away from the axes. A functional version of this Chung-type law is also provided.

Keywords: Fractional Brownian motion; Gaussian random fields; Small deviations; Spectral representation; Chung’s law of the iterated logarithm; 60F17; 60G60; 60G17; 60G15; 60G22; 28C20 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-016-0694-4

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