scholarly journals Continuity and strict positivity of the multi-layer extension of the stochastic heat equation

2020 ◽  
Vol 25 (0) ◽  
Author(s):  
Chin Hang Lun ◽  
Jon Warren
Keyword(s):  
Heat Equation ◽  
Stochastic Heat Equation ◽  
Strict Positivity ◽  
The Stochastic Heat Equation

scholarly journals On the (strict) positivity of solutions of the stochastic heat equation

2014 ◽  
Vol 42 (4) ◽  
pp. 1635-1643 ◽  
Author(s):  
Gregorio R. Moreno Flores
Keyword(s):  
Heat Equation ◽  
Stochastic Heat Equation ◽  
Strict Positivity ◽  
Positivity Of Solutions ◽  
The Stochastic Heat Equation

scholarly journals Dynkin’s Isomorphism Theorem and the Stochastic Heat Equation

2010 ◽  
Vol 34 (3) ◽  
pp. 243-260
Author(s):  
Nathalie Eisenbaum ◽  
Mohammud Foondun ◽  
Davar Khoshnevisan
Keyword(s):  
Heat Equation ◽  
Stochastic Heat Equation ◽  
Isomorphism Theorem ◽  
The Stochastic Heat Equation

scholarly journals Initial measures for the stochastic heat equation

2014 ◽  
Vol 50 (1) ◽  
pp. 136-153 ◽  
Author(s):  
Daniel Conus ◽  
Mathew Joseph ◽  
Davar Khoshnevisan ◽  
Shang-Yuan Shiu
Keyword(s):  
Heat Equation ◽  
Stochastic Heat Equation ◽  
The Stochastic Heat Equation

scholarly journals Gaussian fluctuations for the stochastic heat equation with colored noise

2019 ◽  
Vol 8 (2) ◽  
pp. 402-421
Author(s):  
Jingyu Huang ◽  
David Nualart ◽  
Lauri Viitasaari ◽  
Guangqu Zheng
Keyword(s):  
Heat Equation ◽  
Colored Noise ◽  
Stochastic Heat Equation ◽  
Gaussian Fluctuations ◽  
The Stochastic Heat Equation

scholarly journals Solution of the Stochastic Heat Equation with Nonlinear Losses Using Wiener-Hermite Expansion

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed A. El-Beltagy ◽  
Noha A. Al-Mulla
Keyword(s):  
Heat Equation ◽  
Perturbation Technique ◽  
Stochastic Heat Equation ◽  
Nonlinear Pdes ◽  
Deterministic System ◽  
Hermite Expansion ◽  
Expansion Technique ◽  
Stochastic Solution ◽  
The Stochastic Heat Equation ◽  
Non Gaussian

In the current work, the Wiener-Hermite expansion (WHE) is used to solve the stochastic heat equation with nonlinear losses. WHE is used to deduce the equivalent deterministic system up to third order accuracy. The solution of the equivalent deterministic system is obtained using different techniques numerically and analytically. The finite-volume method (FVM) with Pickard iteration is used to solve the equivalent system iteratively. The WHE with perturbation technique (WHEP) is applied to deduce more simple and decoupled equivalent deterministic system that can be solved numerically without iterations. The system resulting from WHEP technique is solved also analytically using the eigenfunction expansion technique. The Monte-Carlo simulations (MCS) are performed to get the statistical properties of the stochastic solution and to verify other solution techniques. The results show that higher-order solutions are essential especially in case of nonlinearities where non-Gaussian effects cannot be neglected. The comparisons show the efficiency of the numerical WHE and WHEP techniques in solving stochastic nonlinear PDEs compared with the analytical solution and MCS.

scholarly journals Weak Order for the Discretization of the Stochastic Heat Equation Driven by Impulsive Noise

2012 ◽  
Vol 38 (2) ◽  
pp. 345-379 ◽  
Author(s):  
Felix Lindner ◽  
René L. Schilling
Keyword(s):  
Heat Equation ◽  
Impulsive Noise ◽  
Weak Order ◽  
Stochastic Heat Equation ◽  
The Stochastic Heat Equation

scholarly journals Two-point Correlation Function and Feynman-Kac Formula for the Stochastic Heat Equation

2016 ◽  
Vol 46 (4) ◽  
pp. 779-797 ◽  
Author(s):  
Le Chen ◽  
Yaozhong Hu ◽  
David Nualart
Keyword(s):  
Correlation Function ◽  
Heat Equation ◽  
Stochastic Heat Equation ◽  
Point Correlation ◽  
Point Correlation Function ◽  
The Stochastic Heat Equation
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