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Gaussian limiting behavior of the rescaled solution to the linear Korteweg-de vries equation with random initial conditions
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In this paper, the authors analyzed the asymptotic behavior of the rescaled solution to the linear Korteweg-de Vries equation when the initial conditions are supposed to be random and weakly dependent.Abstract:
We analyze the asymptotic behavior of the rescaled solution to the linear Korteweg–de Vries equation when the initial conditions are supposed to be random and weakly dependent. By means of the method of moments we prove the Gaussianity of the limiting process and we present its correlation function. The same technique is applied to the analysis of another third-order heat-type equation.read more
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Spectral Analysis of Fractional Kinetic Equations with Random Data
Vo Anh,Nikolai Leonenko +1 more
TL;DR: In this paper, a spectral representation of the mean-square solution of the fractional kinetic equation (also known as fractional diffusion equation) with random initial condition is presented. But the spectral representation is not suitable for the case of non-Gaussian limiting distributions.
A Complete Bibliography of the Journal of Statistical Physics: 2000{2009
TL;DR: In this paper, Zuc11b et al. this paper showed that 1 ≤ p ≤ ∞ [Dud13]. 1/f [HPF15], 1/n [Per17] and 1/m [DFL17] were the most frequent p ≤ p ≥ ∞.
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Quantitative Breuer-Major Theorems
TL;DR: In this paper, the authors derived explicit upper bounds for quantities of the type |E [ h ( S n ] − E [ h( S ) ] |, where h is a sufficiently smooth test function.
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Quantitative Breuer-Major Theorems
TL;DR: In this paper, the authors derived explicit upper bounds for quantities of the type $|E[h(S_n)] -\E[H(S)]|, where h$ is a sufficiently smooth test function.
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Harmonic analysis of random fractional diffusion-wave equations
Vo Anh,Nikolai Leonenko +1 more
TL;DR: The Green functions and spectral representations of the mean-square solutions of the fractional diffusion-wave equations with random initial conditions are presented.
References
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Book
Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences
TL;DR: The Handbook of Stochastic Methods as mentioned in this paper covers the foundations of Markov systems, stochastic differential equations, Fokker-Planck equations, approximation methods, chemical master equations, and quatum-mechanical Markov processes.
Journal Article
Handbook of stochastic methods for physics, chemistry and the natural sciences, second edition
TL;DR: The Handbook of Stochastic Methods covers systematically and in simple language the foundations of Markov systems, stochastic differential equations, Fokker-Planck equations, approximation methods, chemical master equations, and quatum-mechanical Markov processes.
Book
Solitons: An Introduction
P. G. Drazin,Robin Johnson +1 more
TL;DR: In this article, the authors introduce the Inverse Scattering Transform (IST) and its application in the theory of solitons and its applications to nonlinear systems that arise in the physical sciences.
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