scholarly journals Parameter Estimates and Exact Variations for Stochastic Heat Equations Driven by Space-Time White Noise

2007 ◽  
Vol 25 (3) ◽  
pp. 593-611 ◽  
Author(s):  
Jan Pospíšil ◽  
Roger Tribe
Keyword(s):  
White Noise ◽  
Space Time ◽  
Parameter Estimates ◽  
Heat Equations ◽  
Stochastic Heat Equations

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.

scholarly journals A White Noise Approach to a Class of Non-linear Stochastic Heat Equations

1997 ◽  
Vol 146 (2) ◽  
pp. 382-415 ◽  
Author(s):  
F.E. Benth ◽  
T. Deck ◽  
J. Potthoff
Keyword(s):  
White Noise ◽  
Heat Equations ◽  
Non Linear ◽  
Stochastic Heat Equations
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