scholarly journals On Space-Time Regularity for the Stochastic Heat Equation on Lie Groups

1999 ◽  
Vol 169 (2) ◽  
pp. 559-603 ◽  
Author(s):  
Samy Tindel ◽  
Frederi Viens
Keyword(s):  
Heat Equation ◽  
Lie Groups ◽  
Space Time ◽  
Stochastic Heat Equation ◽  
The Stochastic Heat Equation

scholarly journals Strong rates of convergence for a space-time discretization of the backward stochastic heat equation, and of a linear-quadratic control problem for the stochastic heat equation

2021 ◽  
Author(s):  
Andreas Prohl ◽  
Yanqing Wang
Keyword(s):  
Heat Equation ◽  
Control Problem ◽  
Time Discretization ◽  
Rates Of Convergence ◽  
Space Time ◽  
Stochastic Heat Equation ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
The Stochastic Heat Equation ◽  
Linear Quadratic Control Problem

We verify strong rates of convergence for a time-implicit, finite-element based space-time discretization of the backward stochastic heat equation, and the forward-backward stochastic heat equation from stochastic optimal control. The fully discrete version of the forward-backward stochastic heat equation is then used within a gradient descent algorithm to approximately solve the linear-quadratic control problem for the stochastic heat equation driven by additive noise. This work is thus giving a theoretical foundation for the computational findings in [ 14 ].

scholarly journals Spatial Moduli of Non-Differentiability for Linearized Kuramoto–Sivashinsky SPDEs and Their Gradient

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1251
Author(s):  
Wensheng Wang
Keyword(s):  
Heat Equation ◽  
White Noise ◽  
Fourth Order ◽  
Gaussian Processes ◽  
Three Dimensional ◽  
Space Time ◽  
Symmetry Analysis ◽  
Stochastic Heat Equation ◽  
Moduli Of Continuity

We investigate spatial moduli of non-differentiability for the fourth-order linearized Kuramoto–Sivashinsky (L-KS) SPDEs and their gradient, driven by the space-time white noise in one-to-three dimensional spaces. We use the underlying explicit kernels and symmetry analysis, yielding spatial moduli of non-differentiability for L-KS SPDEs and their gradient. This work builds on the recent works on delicate analysis of regularities of general Gaussian processes and stochastic heat equation driven by space-time white noise. Moreover, it builds on and complements Allouba and Xiao’s earlier works on spatial uniform and local moduli of continuity of L-KS SPDEs and their gradient.

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
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