Brownian bridge asymptotics for random mappings

1992 ◽  
Vol 24 (4) ◽  
pp. 763-764
Author(s):  
D. J. Aldous
Keyword(s):  
Brownian Bridge ◽  
Random Mappings

scholarly journals On the local time density of the reflecting Brownian bridge

2000 ◽  
Vol 13 (2) ◽  
pp. 125-136 ◽  
Author(s):  
Bernhard Gittenberger ◽  
Guy Louchard
Keyword(s):  
Limit Theorem ◽  
Local Time ◽  
Brownian Bridge ◽  
Direct Method ◽  
Random Mappings ◽  
A Direct Method ◽  
Time Density

Expressions for the multi-dimensional densities of Brownian bridge local time are derived by two different methods: A direct method based on Kac's formula for Brownian functionals and an indirect one based on a limit theorem for strata of random mappings.

Brownian bridge asymptotics for random mappings

1994 ◽  
Vol 5 (4) ◽  
pp. 487-512 ◽  
Author(s):  
David J. Aldous ◽  
Jim Pitman
Keyword(s):  
Brownian Bridge ◽  
Random Mappings

Random Mappings and Decompositions of Finite Sets

1972 ◽  
Vol 17 (1) ◽  
pp. 132-145 ◽  
Author(s):  
B. A. Sevast’yanov
Keyword(s):  
Finite Sets ◽  
Random Mappings

Functionals of random mappings: exact and asymptotic results

1991 ◽  
Vol 23 (3) ◽  
pp. 437-455 ◽  
Author(s):  
P. J. Donnelly ◽  
W. J. Ewens ◽  
S. Padmadisastra
Keyword(s):  
Frequency Spectrum ◽  
Exact Results ◽  
Asymptotic Results ◽  
Number Of Components ◽  
Random Mapping ◽  
Random Mappings ◽  
Simulation Results ◽  
Central Tool

A random mapping partitions the set {1, 2, ···, m} into components, where i and j are in the same component if some functional iterate of i equals some functional iterate of j. We consider various functionals of these partitions and of samples from it, including the number of components of ‘small' size and of size O(m) as m → ∞the size of the largest component, the number of components, and various symmetric functionals of the normalized component sizes. In many cases exact results, while available, are uniformative, and we consider various approximations. Numerical and simulation results are also presented. A central tool for many calculations is the ‘frequency spectrum', both exact and asymptotic.

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