Properties of integrals with respect to fractional Poisson processes with compact kernels

Mishura, Y.; Zubchenko, V.

doi:10.1090/S0094-9000-2015-00941-8

Properties of integrals with respect to fractional Poisson processes with compact kernels

Authors: Y. Mishura and V. Zubchenko
Journal: Theor. Probability and Math. Statist. 89 (2014), 143-152
MSC (2010): Primary 60G22; Secondary 60G51
DOI: https://doi.org/10.1090/S0094-9000-2015-00941-8
Published electronically: January 26, 2015
MathSciNet review: 3235181
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Abstract: Properties of a fractional Poisson process with the Molchan–Golosov kernel are studied. The kernel can be viewed as compact since it is non-zero on a compact interval. The integral of a nonrandom function with respect to centered and non-centered fractional Poisson processes with the Molchan–Golosov kernel is introduced. The second moments of these integrals are obtained in terms of the norm of the integrand in the space $L_{1/H}([0,T])$. Moment estimates for higher moments of these integrals are established by using the Bichteler–Jacod inequality.

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