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Levy-type Stochastic Integrals with Regularly Varying Tails

Summary: LŽevy-type Stochastic Integrals with Regularly
Varying Tails
David Applebaum

Probability and Statistics Department,
University of Sheffield,
Hicks Building, Hounsfield Road,
Sheffield, England, S3 7RH
e-mail: D.Applebaum@sheffield.ac.uk
LŽevy-type stochastic integrals M = (M(t), t 0) are obtained by
integrating suitable predictable mappings against Brownian motion
B and an independent Poisson random measure N. We establish
conditions under which the right tails of M are of regular variation.
In particular we require that the intensity measure associated to N
is the product of a regularly varying LŽevy measure with Lebesgue
measure. Both univariate and multivariate versions of the problem
are considered.
Keywords and phrases: LŽevy-type stochastic integral, predictable mapping,
semimartingale, regular variation, LŽevy measure.


Source: Applebaum, David - Department of Probability and Statistics, University of Sheffield


Collections: Mathematics