The local time density estimator

1998 ◽  
pp. 145-167
Author(s):  
D. Bosq
Keyword(s):  
Local Time ◽  
Density Estimator ◽  
Time Density

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.

The Brownian excursion multi-dimensional local time density

1999 ◽  
Vol 36 (2) ◽  
pp. 350-373 ◽  
Author(s):  
Bernhard Gittenberger ◽  
Guy Louchard
Keyword(s):  
Limit Theorem ◽  
Local Time ◽  
Direct Method ◽  
Brownian Excursion ◽  
A Direct Method ◽  
Time Density

Expressions for the multi-dimensional densities of Brownian excursion 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 Galton–Watson trees.

scholarly journals ASYMPTOTIC THEORY FOR LOCAL TIME DENSITY ESTIMATION AND NONPARAMETRIC COINTEGRATING REGRESSION

2009 ◽  
Vol 25 (3) ◽  
pp. 710-738 ◽  
Author(s):  
Qiying Wang ◽  
Peter C.B. Phillips
Keyword(s):  
Density Estimation ◽  
Local Time ◽  
Asymptotic Theory ◽  
Time Estimation ◽  
Fourier Integral ◽  
Limit Theory ◽  
Integral Methods ◽  
Alternative Approach ◽  
Integrated Time Series ◽  
Time Density

Asymptotic theory is developed for local time density estimation for a general class of functionals of integrated and fractionally integrated time series. The main result provides a convenient basis for developing a limit theory for nonparametric cointegrating regression and nonstationary autoregression. The treatment directly involves local time estimation and the density function of the processes under consideration, providing an alternative approach to the Markov chain and Fourier integral methods that have been used in other recent work on these problems.

The Brownian excursion multi-dimensional local time density

1999 ◽  
Vol 36 (02) ◽  
pp. 350-373 ◽  
Author(s):  
Bernhard Gittenberger ◽  
Guy Louchard
Keyword(s):  
Limit Theorem ◽  
Local Time ◽  
Direct Method ◽  
Brownian Excursion ◽  
A Direct Method ◽  
Time Density

Expressions for the multi-dimensional densities of Brownian excursion 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 Galton–Watson trees.

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