Functional Limit Theorems for C-R Increments of k-Dimensional Brownian Motion in Hölder Norm

2000 ◽  
Vol 16 (4) ◽  
pp. 637-654 ◽  
Author(s):  
Qicai Wei
Keyword(s):  
Brownian Motion ◽  
Limit Theorems ◽  
Functional Limit ◽  
Functional Limit Theorems ◽  
Hölder Norm

Functional Limit Theorems for d–dimensional FBM in Hölder Norm

2006 ◽  
Vol 22 (6) ◽  
pp. 1767-1780 ◽  
Author(s):  
Zheng Yan Lin* ◽  
Wen Sheng Wang** ◽  
Kyo Shin Hwang***
Keyword(s):  
Limit Theorems ◽  
Functional Limit ◽  
Functional Limit Theorems ◽  
Hölder Norm

Embedded renewal processes in the GI/G/s queue

1972 ◽  
Vol 9 (3) ◽  
pp. 650-658 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Limit Theorems ◽  
Sufficient Conditions ◽  
Interarrival Time ◽  
Renewal Processes ◽  
Positive Probability ◽  
Functional Limit ◽  
Light Traffic ◽  
Functional Limit Theorems ◽  
Cumulative Processes ◽  
Rule Out

The stable GI/G/s queue (ρ < 1) is sometimes studied using the “fact” that epochs just prior to an arrival when all servers are idle constitute an embedded persistent renewal process. This is true for the GI/G/1 queue, but a simple GI/G/2 example is given here with all interarrival time and service time moments finite and ρ < 1 in which, not only does the system fail to be empty ever with some positive probability, but it is never empty. Sufficient conditions are then given to rule out such examples. Implications of embedded persistent renewal processes in the GI/G/1 and GI/G/s queues are discussed. For example, functional limit theorems for time-average or cumulative processes associated with a large class of GI/G/s queues in light traffic are implied.

Sign in / Sign up

Export Citation Format

Share Document