Convolution equivalence and infinite divisibility

Anthony G. Pakes

144 citations0/0 files storedJournal of Applied Probability

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Probability and Risk Models Probability and Statistical Research Stochastic processes and financial applications

Abstract

Known results relating the tail behaviour of a compound Poisson distribution function to that of its Lévy measure when one of them is convolution equivalent are extended to general infinitely divisible distributions. A tail equivalence result is obtained for random sum distributions in which the summands have a two-sided distribution.

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References

2001Stochastic Processes for Insurance and Finance 1999Stochastic Processes for Insurance & Finance 1992Generalized Gamma Convolutions and Related Classes of Distributions and Densities 1988Subexponential distributions and integrated tails 1979Subexponentiality and infinite divisibility 1980On closure and factorization properties of subexponential and related distributions 1975The Class of Subexponential Distributions 1986Convolution tails, product tails and domains of attraction

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2007Lower limits and equivalences for convolution tails 2008From light tails to heavy tails through multiplier 2010Ratio of the Tail of an Infinitely Divisible Distribution on the Line to that of its Lévy Measure 2007The subexponentiality of products revisited 2006Extremal behavior of stochastic volatility models 2008On the asymptotic behaviour of Lévy processes, Part I: Subexponential and exponential processes

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