Asymptotics of randomly stopped sums in the presence of heavy tails
Asymptotics of randomly stopped sums in the presence of heavy tails
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International Statistical Institute and Bernoulli Society for Mathematical Statistics and Probability
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English
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International Statistical Institute and Bernoulli Society for Mathematical Statistics and Probability
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We study conditions under which P{S τ > x} ∼ P {M τ > x} ∼ EτP {ξ₁ > x} as x → ∞, where S τ is a sum ξ₁ + ··· + ξ τ of random size τ and M τ is a maximum of partial sums M τ = max n≤τ S n . Here, ξ n , n = 1, 2, …, are independent identically distributed random variables whose common distribution is assumed to be subexponential. We mostly consider...
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Full title
Asymptotics of randomly stopped sums in the presence of heavy tails
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TN_cdi_projecteuclid_primary_oai_CULeuclid_euclid_bj_1290092892
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https://devfeature-collection.sl.nsw.gov.au/record/TN_cdi_projecteuclid_primary_oai_CULeuclid_euclid_bj_1290092892
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ISSN
1350-7265
DOI
10.3150/10-BEJ251
