scholarly journals Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise

2020 ◽  
Vol 38 (4) ◽  
pp. 747-768
Author(s):  
Randall Herrell ◽  
Renming Song ◽  
Dongsheng Wu ◽  
Yimin Xiao
Keyword(s):  
Heat Equation ◽  
Colored Noise ◽  
Space Time ◽  
Stochastic Heat Equation

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.

Recent developments on stochastic heat equation with additive fractional-colored noise

2014 ◽  
Vol 17 (1) ◽  
Author(s):  
Ciprian Tudor
Keyword(s):  
Comparative Study ◽  
Heat Equation ◽  
Gaussian Noise ◽  
Colored Noise ◽  
Covariance Structure ◽  
Stochastic Heat Equation ◽  
Basic Properties ◽  
Recent Developments

AbstractWe expose some recent and less recent results related to the existence and the basic properties of the solution to the linear stochastic heat equation with additive Gaussian noise. We will make a comparative study of the behavior of the solution in function of the covariance structure of the driving noise.

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