Article ID Journal Published Year Pages File Type
1156027 Stochastic Processes and their Applications 2010 28 Pages PDF
Abstract

Cramér’s theorem provides an estimate for the tail probability of the maximum of a random walk with negative drift and increments having a moment generating function finite in a neighborhood of the origin. The class of (g,F)(g,F)-processes generalizes in a natural way random walks and fractional ARIMA models used in time series analysis. For those (g,F)(g,F)-processes with negative drift, we obtain a logarithmic estimate of the tail probability of their maximum, under conditions comparable to Cramér’s. Furthermore, we exhibit the most likely paths as well as the most likely behavior of the innovations leading to a large maximum.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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