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.

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.

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.

scholarly journals The Width of Galton-Watson Trees Conditioned by the Size

2004 ◽  
Vol Vol. 6 no. 2 ◽  
Author(s):  
Michael Drmota ◽  
Bernhard Gittenberger
Keyword(s):  
Limit Theorem ◽  
Local Time ◽  
Weak Limit ◽  
Brownian Excursion ◽  
International Audience ◽  
Weak Limit Theorem

International audience It is proved that the moments of the width of Galton-Watson trees of size n and with offspring variance σ ^2 are asymptotically given by (σ √n)^pm_p where m_p are the moments of the maximum of the local time of a standard scaled Brownian excursion. This is done by combining a weak limit theorem and a tightness estimate. The method is quite general and we state some further applications.

scholarly journals Plastic waste to fuels by hydrocracking at mild conditions

2021 ◽  
Vol 7 (17) ◽  
pp. eabf8283
Author(s):  
Sibao Liu ◽  
Pavel A. Kots ◽  
Brandon C. Vance ◽  
Andrew Danielson ◽  
Dionisios G. Vlachos
Keyword(s):  
Direct Method ◽  
Acid Sites ◽  
Liquid Fuels ◽  
High Yield ◽  
Tandem Catalysis ◽  
Hy Zeolite ◽  
Environmental Threat ◽  
Single Use ◽  
Initial Activation ◽  
A Direct Method

Single-use plastics impose an enormous environmental threat, but their recycling, especially of polyolefins, has been proven challenging. We report a direct method to selectively convert polyolefins to branched, liquid fuels including diesel, jet, and gasoline-range hydrocarbons, with high yield up to 85% over Pt/WO3/ZrO2 and HY zeolite in hydrogen at temperatures as low as 225°C. The process proceeds via tandem catalysis with initial activation of the polymer primarily over Pt, with subsequent cracking over the acid sites of WO3/ZrO2 and HY zeolite, isomerization over WO3/ZrO2 sites, and hydrogenation of olefin intermediates over Pt. The process can be tuned to convert different common plastic wastes, including low- and high-density polyethylene, polypropylene, polystyrene, everyday polyethylene bottles and bags, and composite plastics to desirable fuels and light lubricants.

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