scholarly journals On the completion of Skorokhod space

2020 ◽  
Vol 25 (0) ◽  
Author(s):  
Mikhail Lifshits ◽  
Vladislav Vysotsky
Keyword(s):  
Skorokhod Space

On the convergence of LePage series in Skorokhod space

2012 ◽  
Vol 82 (1) ◽  
pp. 145-150 ◽  
Author(s):  
Youri Davydov ◽  
Clément Dombry
Keyword(s):  
Skorokhod Space

Functional limit theorems for the number of busy servers in a G/G/∞ queue

2018 ◽  
Vol 55 (1) ◽  
pp. 15-29 ◽  
Author(s):  
Alexander Iksanov ◽  
Wissem Jedidi ◽  
Fethi Bouzeffour
Keyword(s):  
Weak Convergence ◽  
Integral Representation ◽  
Gaussian Process ◽  
Limit Theorems ◽  
Functional Limit ◽  
Functional Limit Theorems ◽  
Open Problems ◽  
Skorokhod Space

Abstract We discuss weak convergence of the number of busy servers in a G/G/∞ queue in the J1-topology on the Skorokhod space. We prove two functional limit theorems with random and nonrandom centering, thereby solving two open problems stated in Mikosch and Resnick (2006). A new integral representation for the limit Gaussian process is given.

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