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Activity Number:
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400
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Type:
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Contributed
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Date/Time:
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Wednesday, August 6, 2008 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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| Abstract - #301437 |
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Title:
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On the Maximum of Some Processes with Negative Drift and Heavy Tail Innovations
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Author(s):
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William P. McCormick*+
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Companies:
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The University of Georgia
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Address:
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Statistics Department, Athens, GA, 30602,
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Keywords:
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maximum of random walk ; heavy tail ; fractional ARIMA ; long range dependence
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Abstract:
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A classical result due to Veraverbeke gives the asymptotic tail behavior of the supremum of a random walk with heavy-tail innovations and negative mean. In this talk we will present extensions to this result where the innovations defining the random walk may be dependent. In particular we will allow for innovations constituting a nonstationary FARIMA process. More generally, we discuss how the single large jump heuristic applies in this setting. We also discuss sample path behavior conditionally on the supremum exceeding a large value.
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