Random graphs, random walks, differential equations and the probabilistic analysis of algorithms

1998 ◽  
pp. 1-2 ◽  
Author(s):  
Richard M. Karp
Keyword(s):  
Differential Equations ◽  
Random Walks ◽  
Random Graphs ◽  
Probabilistic Analysis ◽  
Analysis Of Algorithms ◽  
Probabilistic Analysis Of Algorithms

Density approximation and exact simulation of random variables that are solutions of fixed-point equations

2002 ◽  
Vol 34 (2) ◽  
pp. 441-468 ◽  
Author(s):  
Luc Devroye ◽  
Ralph Neininger
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Error Bounds ◽  
Probabilistic Analysis ◽  
Analysis Of Algorithms ◽  
Random Variables ◽  
Probability Measures ◽  
Density Approximation ◽  
Exact Simulation ◽  
Probabilistic Analysis Of Algorithms

An algorithm is developed for exact simulation from distributions that are defined as fixed points of maps between spaces of probability measures. The fixed points of the class of maps under consideration include examples of limit distributions of random variables studied in the probabilistic analysis of algorithms. Approximating sequences for the densities of the fixed points with explicit error bounds are constructed. The sampling algorithm relies on a modified rejection method.

Density approximation and exact simulation of random variables that are solutions of fixed-point equations

2002 ◽  
Vol 34 (02) ◽  
pp. 441-468 ◽  
Author(s):  
Luc Devroye ◽  
Ralph Neininger
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Error Bounds ◽  
Probabilistic Analysis ◽  
Analysis Of Algorithms ◽  
Random Variables ◽  
Probability Measures ◽  
Density Approximation ◽  
Exact Simulation ◽  
Probabilistic Analysis Of Algorithms

An algorithm is developed for exact simulation from distributions that are defined as fixed points of maps between spaces of probability measures. The fixed points of the class of maps under consideration include examples of limit distributions of random variables studied in the probabilistic analysis of algorithms. Approximating sequences for the densities of the fixed points with explicit error bounds are constructed. The sampling algorithm relies on a modified rejection method.

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