scholarly journals Some explicit formulas for the Brownian bridge, Brownian meander and Bessel process under uniform sampling

2015 ◽  
Vol 19 ◽  
pp. 578-589
Author(s):  
Mathieu Rosenbaum ◽  
Marc Yor
Keyword(s):  
Brownian Bridge ◽  
Bessel Process ◽  
Explicit Formulas ◽  
Uniform Sampling ◽  
Brownian Meander

scholarly journals Brownian local times

1995 ◽  
Vol 8 (3) ◽  
pp. 209-232 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Brownian Motion ◽  
Brownian Bridge ◽  
Distribution Functions ◽  
Local Times ◽  
Explicit Formulas ◽  
Brownian Excursion ◽  
Reflecting Brownian Motion ◽  
Brownian Meander

In this paper explicit formulas are given for the distribution functions and the moments of the local times of the Brownian motion, the reflecting Brownian motion, the Brownian meander, the Brownian bridge, the reflecting Brownian bridge and the Brownian excursion.

Limit distributions for the Bernoulli meander

1995 ◽  
Vol 32 (2) ◽  
pp. 375-395 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Random Walk ◽  
Local Time ◽  
Limit Behavior ◽  
Explicit Formulas ◽  
Limit Distributions ◽  
Brownian Meander

This paper is concerned with the distibutions and the moments of the area and the local time of a random walk, called the Bernoulli meander. The limit behavior of the distributions and the moments is determined in the case where the number of steps in the random walk tends to infinity. The results of this paper yield explicit formulas for the distributions and the moments of the area and the local time for the Brownian meander.

Density factorizations for brownian motion, meander and the three-dimensional bessel process, and applications

1984 ◽  
Vol 21 (3) ◽  
pp. 500-510 ◽  
Author(s):  
J.-P. Imhof
Keyword(s):  
Brownian Motion ◽  
Three Dimensional ◽  
Fixed Time ◽  
Bessel Process ◽  
Time Interval ◽  
Change Of Measure ◽  
Fixed Time Interval ◽  
Simple Change ◽  
Brownian Meander ◽  
Passage Times

Joint densities concerning in particular the value and time of the maximum over a fixed time interval, or the behavior over intervals determined by some first- and last-passage times, are determined for Brownian motion, the three-dimensional Bessel process and Brownian meander. Simple change of measure formulas permit easy passage from one process to the other. Examples are given.

Limit distributions for the Bernoulli meander

1995 ◽  
Vol 32 (02) ◽  
pp. 375-395 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Random Walk ◽  
Local Time ◽  
Limit Behavior ◽  
Explicit Formulas ◽  
Limit Distributions ◽  
Brownian Meander

This paper is concerned with the distibutions and the moments of the area and the local time of a random walk, called the Bernoulli meander. The limit behavior of the distributions and the moments is determined in the case where the number of steps in the random walk tends to infinity. The results of this paper yield explicit formulas for the distributions and the moments of the area and the local time for the Brownian meander.

Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process

2017 ◽  
Vol 27 (6) ◽  
Author(s):  
Andrey M. Zubkov ◽  
Maksim P. Savelov
Keyword(s):  
Random Process ◽  
Bessel Process ◽  
Time Change ◽  
Stationary Random Process ◽  
Explicit Formulas ◽  
Joint Distributions ◽  
Finite Dimensional

AbstractIt is shown that, with suitable time change, the finite-dimensional distributions of the process formed by successive values of the Pearson statistics for an expanding sample converge to finite-dimensional distributions of the stationary random process, namely, the normalized square of the Bessel process. The results obtained earlier on the limit joint distributions of the Pearson statistics are used to derive explicit formulas for the density of joint distributions of the Bessel process.

Density factorizations for brownian motion, meander and the three-dimensional bessel process, and applications

1984 ◽  
Vol 21 (03) ◽  
pp. 500-510 ◽  
Author(s):  
J.-P. Imhof
Keyword(s):  
Brownian Motion ◽  
Three Dimensional ◽  
Fixed Time ◽  
Bessel Process ◽  
Time Interval ◽  
Change Of Measure ◽  
Fixed Time Interval ◽  
Simple Change ◽  
Brownian Meander ◽  
Passage Times

Joint densities concerning in particular the value and time of the maximum over a fixed time interval, or the behavior over intervals determined by some first- and last-passage times, are determined for Brownian motion, the three-dimensional Bessel process and Brownian meander. Simple change of measure formulas permit easy passage from one process to the other. Examples are given.

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