Article
Some new equivalent conditions on asymptotics and local asymptotics for random sums and their applications
Department of Mathematics, Soochow University, Suzhou 215006, China; Department of Applied Mathematics, Nanjing Audit University, Nanjing 210029, China; Department of Applied Mathematics, University of Science and Technology of Suzhou, Suzhou 215009, China
Insurance: Mathematics and Economics
DOI:10.1016/j.insmatheco.2006.04.006
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Article: Equivalent conditions of local asymptotics for the overshoot of a random walk with heavy-tailed increments
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ABSTRACT: This article gives the equivalent conditions of the local asymptotics for the overshoot of a random walk with heavy-tailed increments, from which we find that the above asymptotics are different from the local asymptotics for the supremum of the random walk. To do this, the article first extends and improves some existing results about the solutions of renewal equations.Acta Mathematica Scientia. -
Article: Local asymptotics of a Markov modulated random walk with heavy-tailed increments
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ABSTRACT: In this paper, we obtain sufficient and necessary conditions for local asymptotics for the maximum of a Markov modulated random walk with long-tailed increments and negative drifts, where the local asymptotics means asymptotic behaviour of P(· ∈ (x, x + z]) for each z > 0, as x→∞. Our results extend and improve the existing ones in the literature. KeywordsMarkov modulated random walk–local asymptotics–long-tailed distributions–subexponential distributions–Wiener-Hopf factorizationActa Mathematica Sinica 04/2012; 27(9):1843-1854. · 0.47 Impact Factor
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Keywords
existing corresponding results
incorrect lemma
infinite divisibility theory
new equivalent conditions
new method
new results
obtained equivalent conditions
random sums
