On extreme value theory for group stationary Gaussian processes

2018 ◽  
Vol 22 ◽  
pp. 1-18
Author(s):  
Patrik Albin
Keyword(s):  
Gaussian Processes ◽  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value ◽  
Usual Sense ◽  
Stationary Processes ◽  
Topological Groups ◽  
Euclidian Space ◽  
Stationary Gaussian Processes ◽  
Locally Compact Topological Groups

We study extreme value theory of right stationary Gaussian processes with parameters in open subsets with compact closure of (not necessarily Abelian) locally compact topological groups. Even when specialized to Euclidian space our result extend results on extremes of stationary Gaussian processes and fields in the literature by means of requiring weaker technical conditions as well as by means of the fact that group stationary processes need not be stationary in the usual sense (that is, with respect to addition as group operation).

On the supremum distribution of integrated stationary Gaussian processes with negative linear drift

1999 ◽  
Vol 31 (01) ◽  
pp. 135-157 ◽  
Author(s):  
Jinwoo Choe ◽  
Ness B. Shroff
Keyword(s):  
Gaussian Processes ◽  
Extreme Value Theory ◽  
Continuous Time ◽  
Value Theory ◽  
Numerical Examples ◽  
Stationary Increments ◽  
Negative Drift ◽  
Stationary Gaussian Processes ◽  
Continuous Time Processes ◽  
Asymptotic Upper Bound

In this paper we study the supremum distribution of a class of Gaussian processes having stationary increments and negative drift using key results from Extreme Value Theory. We focus on deriving an asymptotic upper bound to the tail of the supremum distribution of such processes. Our bound is valid for both discrete- and continuous-time processes. We discuss the importance of the bound, its applicability to queueing problems, and show numerical examples to illustrate its performance.

On the supremum distribution of integrated stationary Gaussian processes with negative linear drift

1999 ◽  
Vol 31 (1) ◽  
pp. 135-157 ◽  
Author(s):  
Jinwoo Choe ◽  
Ness B. Shroff
Keyword(s):  
Gaussian Processes ◽  
Extreme Value Theory ◽  
Continuous Time ◽  
Value Theory ◽  
Numerical Examples ◽  
Stationary Increments ◽  
Negative Drift ◽  
Stationary Gaussian Processes ◽  
Continuous Time Processes ◽  
Asymptotic Upper Bound

In this paper we study the supremum distribution of a class of Gaussian processes having stationary increments and negative drift using key results from Extreme Value Theory. We focus on deriving an asymptotic upper bound to the tail of the supremum distribution of such processes. Our bound is valid for both discrete- and continuous-time processes. We discuss the importance of the bound, its applicability to queueing problems, and show numerical examples to illustrate its performance.

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