EQUIVALENT CONDITIONS OF LOCAL ASYMPTOTICS FOR THE OVERSHOOT OF A RANDOM WALK WITH HEAVY-TAILED INCREMENTS |
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| Authors: | Wang Kaiyong Wang Yuebao Yin Chuancun |
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| Institution: | Wang Kaiyong 1,2 Wang Yuebao 1 Yin Chuancun 3 1. Department of Mathematics,Soochow University,Suzhou 215006,China 2. School of Mathematics and Physics,Suzhou University of Science and Technology,Suzhou 215009,China 3. Department of Mathematics,Qufu Normal University,Qufu 273165,China |
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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. |
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| Keywords: | Equivalent conditions asymptotics random walk renewal equation |
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