Upper-bounds for tail probability of a queue with long-range dependent input

2002 ◽  
Author(s):  
N. Rananand
Keyword(s):  
Long Range ◽  
Tail Probability ◽  
Upper Bounds

scholarly journals Upper bounds on transport exponents for long-range operators

2021 ◽  
Vol 62 (7) ◽  
pp. 073506
Author(s):  
Svetlana Jitomirskaya ◽  
Wencai Liu
Keyword(s):  
Long Range ◽  
Upper Bounds

On the extinction time distribution of a branching process in varying environments

1980 ◽  
Vol 12 (2) ◽  
pp. 350-366 ◽  
Author(s):  
Tetsuo Fujimagari
Keyword(s):  
Generating Functions ◽  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Tail Probability ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Extinction Time ◽  
Asymptotic Formulae ◽  
Varying Environments

The extinction time distributions of a class of branching processes in varying environments are considered. We obtain (i) sufficient conditions for the extinction probability q = 1 or q < 1; (ii) asymptotic formulae for the tail probability of the extinction time if q = 1; and (iii) upper bounds for 1 – q if q < 1. To derive these results, we give upper and lower bounds for the tail probability of the extinction time. For the proofs, we use a method that compares probability generating functions with fractional linear generating functions.

On the extinction time distribution of a branching process in varying environments

1980 ◽  
Vol 12 (02) ◽  
pp. 350-366 ◽  
Author(s):  
Tetsuo Fujimagari
Keyword(s):  
Generating Functions ◽  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Tail Probability ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Extinction Time ◽  
Asymptotic Formulae ◽  
Varying Environments

The extinction time distributions of a class of branching processes in varying environments are considered. We obtain (i) sufficient conditions for the extinction probability q = 1 or q &lt; 1; (ii) asymptotic formulae for the tail probability of the extinction time if q = 1; and (iii) upper bounds for 1 – q if q &lt; 1. To derive these results, we give upper and lower bounds for the tail probability of the extinction time. For the proofs, we use a method that compares probability generating functions with fractional linear generating functions.

scholarly journals Polynomial tails of additive-type recursions

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Eva-Maria Schopp
Keyword(s):  
Tail Probability ◽  
Upper Bounds ◽  
Random Trees ◽  
Divide And Conquer ◽  
Variation Theory ◽  
Recursive Sequences ◽  
Recursive Structures ◽  
International Audience ◽  
Asymptotic Tail Probability ◽  
Polynomial Bounds

International audience Polynomial bounds and tail estimates are derived for additive random recursive sequences, which typically arise as functionals of recursive structures, of random trees, or in recursive algorithms. In particular they arise as parameters of divide and conquer type algorithms. We mainly focuss on polynomial tails that arise due to heavy tail bounds of the toll term and the starting distributions. Besides estimating the tail probability directly we use a modified version of a theorem from regular variation theory. This theorem states that upper bounds on the asymptotic tail probability can be derived from upper bounds of the Laplace―Stieltjes transforms near zero.

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