The law of the iterated logarithm for the solution of the Burgers equation with random initial data

1998 ◽  
Vol 64 (6) ◽  
pp. 704-713 ◽  
Author(s):  
Yu. Yu. Bakhtin
Keyword(s):  
Initial Data ◽  
Burgers Equation ◽  
Random Initial Data ◽  
Iterated Logarithm ◽  
The Law

scholarly journals Using random walks to establish wavelike behavior in a linear FPUT system with random coefficients

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Joshua A. McGinnis ◽  
J. Douglas Wright
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Random Walks ◽  
Random Coefficients ◽  
Energy Estimates ◽  
Stochastic Homogenization ◽  
Iterated Logarithm ◽  
Long Wave ◽  
The Law ◽  
Spatially Varying

<p style='text-indent:20px;'>We consider a linear Fermi-Pasta-Ulam-Tsingou lattice with random spatially varying material coefficients. Using the methods of stochastic homogenization we show that solutions with long wave initial data converge in an appropriate sense to solutions of a wave equation. The convergence is strong and both almost sure and in expectation, but the rate is quite slow. The technique combines energy estimates with powerful classical results about random walks, specifically the law of the iterated logarithm.</p>

scholarly journals The Law of the Iterated Logarithm for a Markov Process

1970 ◽  
Vol 41 (3) ◽  
pp. 945-955 ◽  
Author(s):  
R. P. Pakshirajan ◽  
M. Sreehari
Keyword(s):  
Markov Process ◽  
Iterated Logarithm ◽  
The Law

Extreme values and the law of the iterated logarithm

1987 ◽  
Vol 74 (3) ◽  
pp. 319-340 ◽  
Author(s):  
J. Kuelbs ◽  
M. Ledoux
Keyword(s):  
Extreme Values ◽  
Iterated Logarithm ◽  
The Law

The law of the Iterated Logarithm for random interval homeomorphisms

2021 ◽  
Author(s):  
Klaudiusz Czudek ◽  
Tomasz Szarek ◽  
Hanna Wojewódka-Ściążko
Keyword(s):  
Random Interval ◽  
Iterated Logarithm ◽  
The Law
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