Representation Results of Intrinsic Location Functionals

• Activity Number: 635
• Type: Topic Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Yi Shen*+
• Companies: University of Waterloo
• Keywords: random locations ; stationary processes ; supremum location ; ordered random set

Abstract

Intrinsic location functional is a large class of random locations including the location of path supremum/infimum over a compact interval, the first/last hitting times, the location of the largest jump, etc. It has been shown that the class of intrinsic location functionals possesses rich distributional properties for stationary processes. On the other hand, these properties can be used to characterize the stationarity and other related behaviors of the process. In the current work we develop two representation results for intrinsic location functionals, using partially ordered random sets and a special type of piecewise linear functions. The results indicate that any intrinsic location functional can be regarded as the location of the maximal element over the interval of interest according to certain order, and that the relative location of an intrinsic location functional changes in a very specific way when the interval moves along the real line. Finally we discuss the applications of these results, especially a potential link between the intrinsic location functionals and the queueing systems with deadline.