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Moment Comparison of Multilinear Forms in Stable and Semistable Random Variables with Application to Semistable Multiple Integrals

  • Balram S. Rajput
  • Kavi Rama-Murthy
  • Xavier R. Retnam
Part of the Trends in Mathematics book series (TM)

Abstract

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 phrases

Tail probabilities and moment comparisons stable and semistable random measures stable and semistable multiple integrals 

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Balram S. Rajput
    • 1
  • Kavi Rama-Murthy
    • 2
  • Xavier R. Retnam
    • 3
  1. 1.Department of MathematicsUniversity of TennesseeKnoxvilleUSA
  2. 2.Indian Statistical InstituteBangaloreIndia
  3. 3.Department of MathematicsBlue Mountain CollegeBlue MountainUSA

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