scholarly journals Local theorems for arithmetic compound renewal processes when Cramer's condition holds

2019 ◽  
Vol 16 ◽  
pp. 21-41 ◽  
Author(s):  
A. A. Mogulskii
Keyword(s):  
Renewal Processes ◽  
Cramér’S Condition ◽  
Compound Renewal Processes

Invariance principles in queueing theory

1989 ◽  
Vol 26 (04) ◽  
pp. 845-857
Author(s):  
Michael Alex ◽  
Josef Steinebach
Keyword(s):  
Convergence Rate ◽  
Stochastic Processes ◽  
Queueing Theory ◽  
Counting Process ◽  
Heavy Traffic ◽  
Renewal Processes ◽  
Light Traffic ◽  
Invariance Principles ◽  
Renewal Counting Process ◽  
Compound Renewal Processes

Several stochastic processes in queueing theory are based upon compound renewal processes . For queues in light traffic, however, the summands {Xk }and the renewal counting process {N(t)} are typically dependent on each other. Making use of recent invariance principles for such situations, we present some weak and strong approximations for the GI/G/1 queues in light and heavy traffic. Some applications are discussed including convergence rate statements or Darling–Erdös-type extreme value theorems for the processes under consideration.

scholarly journals On the convergence of quadratic variation for compound fractional Poisson processes

2012 ◽  
Vol 15 (2) ◽  
Author(s):  
Enrico Scalas ◽  
Noèlia Viles
Keyword(s):  
Stochastic Process ◽  
Random Variable ◽  
Quadratic Variation ◽  
Poisson Processes ◽  
Renewal Processes ◽  
The Relationship ◽  
Compound Renewal Processes

AbstractThe relationship between quadratic variation for compound renewal processes and M-Wright functions is discussed. The convergence of quadratic variation is investigated both as a random variable (for given t) and as a stochastic process.

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