scholarly journals New results on pathwise uniqueness for the heat equation with colored noise

2013 ◽  
Vol 18 (0) ◽  
Author(s):  
Thomas Rippl ◽  
Anja Sturm
Keyword(s):  
Heat Equation ◽  
Colored Noise ◽  
Pathwise Uniqueness

scholarly journals Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Wensheng Wang ◽  
Xiaoying Chang ◽  
Wang Liao
Keyword(s):  
Heat Equation ◽  
White Noise ◽  
Harmonic Analysis ◽  
Central Limit ◽  
Gaussian Processes ◽  
Limit Theorems ◽  
Colored Noise ◽  
Asymptotic Distributions ◽  
Heat Equations ◽  
Stochastic Heat Equations

Let u α , d = u α , d t , x ,   t ∈ 0 , T , x ∈ ℝ d be the solution to the stochastic heat equations (SHEs) with spatially colored noise. We study the realized power variations for the process u α , d , in time, having infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for SHEs with spatially colored noise. This work builds on the recent works on delicate analysis of variations of general Gaussian processes and SHEs driven by space-time white noise.

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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