Tail expansions for the distribution of the maximum of a random walk with negative drift and regularly varying increments
نویسندگان
چکیده
منابع مشابه
The Maximum on a Random Time Interval of a Random Walk with Long-tailed Increments and Negative Drift
Random walks with long-tailed increments have many important applications in insurance, finance, queueing networks, storage processes, and the study of extreme events in nature and elsewhere. See, for example, Embrechts et al. (1997), Asmussen (1998, 1999) and Greiner et al. (1999) for some background. In this paper we study the distribution of the maximum of such a random walk over a random ti...
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Let S,, n > 1, be the partial sums of i.i.d. random variables with negative mean value. Many papers (see, for example, [l, 2,5,6,7,9,11]) give us different theorems on the tail behavior of the distribution of sup{&, n > 1). In this paper the final versions of these theorems (with necessary and sufficient conditions) are presented. The main attention is paid to the necessity part of these theorems.
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15 صفحه اولThe Limit Distribution of the Maximum Increment of a Random Walk with Dependent Regularly Varying Jump Sizes
We investigate the maximum increment of a random walk with heavy-tailed jump size distribution. Here heavy-tailedness is understood as regular variation of the finite-dimensional distributions. The jump sizes constitute a strictly stationary sequence. Using a continuous mapping argument acting on the point processes of the normalized jump sizes, we prove that the maximum increment of the random...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2007
ISSN: 0304-4149
DOI: 10.1016/j.spa.2007.03.004