Some new equivalent conditions on asymptotics and local asymptotics for random sums and their applications
ABSTRACT This paper uses a new method to achieve some new equivalent conditions on asymptotics and local asymptotics for random sums, modifies some results based on an incorrect lemma, and cancels some technical conditions on the existing corresponding results. The newly obtained equivalent conditions are applied to risk theory and infinite divisibility theory, and some new results are derived.
Article: Equivalent conditions of local asymptotics for the overshoot of a random walk with heavy-tailed increments[show abstract] [hide abstract]
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.
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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