Moment Comparison of Multilinear Forms in Stable and Semistable Random Variables with Application to Semistable Multiple Integrals
Let 1 < α< 2. We provide a uniform comparison of the tail probabilities of (non-symmetric) strictly α-semistable random variables with the tail probabilities of their symmetrized counterparts as well as of their “associated” strictly & symmetric α-stable random variables. We use this to obtain a uniform comparison between the moments of the multilinear forms in (non-symmetric) strictly α-semistable random variables on the one hand and in their symmetrized counterparts as well as in their “associated” strictly, & symmetric α-stable random variables on the other. In turn, using this and following the approach of Krakowiak and Szulga in the stable case, we construct strictly and symmetric α-semistable multiple stochastic integrals of Banach space-valued integrands.
Keywords and phrasesTail probabilities and moment comparisons stable and semistable random measures stable and semistable multiple integrals
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