scholarly journals Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise

2019 ◽  
Vol 24 (0) ◽  
Author(s):  
Raluca M. Balan ◽  
Lluís Quer-Sardanyons ◽  
Jian Song
Keyword(s):  
Wave Equation ◽  
Gaussian Noise ◽  
Space Time ◽  
Stochastic Wave Equation

Energy of a string driven by a two-parameter Gaussian noise white in time

2001 ◽  
Vol 38 (04) ◽  
pp. 960-974 ◽  
Author(s):  
Boris P. Belinskiy ◽  
Peter Caithamer
Keyword(s):  
Wave Equation ◽  
Gaussian Noise ◽  
Spatial Dimension ◽  
Spatial Covariance ◽  
Stochastic Wave Equation ◽  
Two Parameter

In this paper we consider the stochastic wave equation in one spatial dimension driven by a two-parameter Gaussian noise which is white in time and has general spatial covariance. We give conditions on the spatial covariance of the driving noise sufficient for the string to have finite expected energy and calculate this energy as a function of time. We show that these same conditions on the spatial covariance of the driving noise are also sufficient to guarantee that the energy of the string has a version which is continuous almost surely.

Energy of a string driven by a two-parameter Gaussian noise white in time

2001 ◽  
Vol 38 (4) ◽  
pp. 960-974 ◽  
Author(s):  
Boris P. Belinskiy ◽  
Peter Caithamer
Keyword(s):  
Wave Equation ◽  
Gaussian Noise ◽  
Spatial Dimension ◽  
Spatial Covariance ◽  
Stochastic Wave Equation ◽  
Two Parameter

In this paper we consider the stochastic wave equation in one spatial dimension driven by a two-parameter Gaussian noise which is white in time and has general spatial covariance. We give conditions on the spatial covariance of the driving noise sufficient for the string to have finite expected energy and calculate this energy as a function of time. We show that these same conditions on the spatial covariance of the driving noise are also sufficient to guarantee that the energy of the string has a version which is continuous almost surely.

scholarly journals Fractional stochastic wave equation driven by a Gaussian noise rough in space

Bernoulli ◽  
2020 ◽  
Vol 26 (4) ◽  
pp. 2699-2726
Author(s):  
Jian Song ◽  
Xiaoming Song ◽  
Fangjun Xu
Keyword(s):  
Wave Equation ◽  
Gaussian Noise ◽  
Stochastic Wave Equation

Spatial variation for the solution to the stochastic linear wave equation driven by additive space-time white noise

2018 ◽  
Vol 18 (05) ◽  
pp. 1850036 ◽  
Author(s):  
M. Khalil ◽  
C. A. Tudor ◽  
M. Zili
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
White Noise ◽  
Space Time ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Stochastic Wave Equation ◽  
Quadratic Variations

We study the asymptotic behavior of the spatial quadratic variation for the solution to the stochastic wave equation driven by additive space-time white noise. We prove that the sequence of its renormalized quadratic variations satisfies a central limit theorem (CLT for short). We obtain the rate of convergence for this CLT via the Stein–Malliavin calculus and we also discuss some consequences.

A space-time BIE method for wave equation problems: the (two-dimensional) Neumann case

2013 ◽  
Vol 34 (1) ◽  
pp. 390-434 ◽  
Author(s):  
S. Falletta ◽  
G. Monegato ◽  
L. Scuderi
Keyword(s):  
Wave Equation ◽  
Space Time ◽  
Two Dimensional
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