White noise in space and time and the cylindrical wiener process

1988 ◽  
Vol 6 (1) ◽  
pp. 81-89 ◽  
Author(s):  
Kay-Uwe Schaumlöffel
Keyword(s):  
White Noise ◽  
Wiener Process ◽  
Space And Time ◽  
Cylindrical Wiener Process

scholarly journals Stochastic energy balance climate models with Legendre weighted diffusion and an additive cylindrical Wiener process forcing

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Gregorio Díaz ◽  
Jesús Ildefonso Díaz
Keyword(s):  
Energy Balance ◽  
Wiener Process ◽  
Climate Models ◽  
Random Parameter ◽  
Parabolic Problems ◽  
Change Of Variables ◽  
Wiener Processes ◽  
Cylindrical Wiener Process ◽  
The Stability ◽  
Suitable Change

<p style='text-indent:20px;'>We consider a class of one-dimensional nonlinear stochastic parabolic problems associated to Sellers and Budyko diffusive energy balance climate models with a Legendre weighted diffusion and an additive cylindrical Wiener processes forcing. Our results use in an important way that, under suitable assumptions on the Wiener processes, a suitable change of variables leads the problem to a pathwise random PDE, hence an essentially "deterministic" formulation depending on a random parameter. Two applications are also given: the stability of solutions when the Wiener process converges to zero and the asymptotic behaviour of solutions for large time.</p>

LARGE DEVIATION ASYMPTOTICS FOR RANDOM-WALK TYPE PERTURBATIONS

2007 ◽  
Vol 07 (01) ◽  
pp. 75-89
Author(s):  
ZHIHUI YANG
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
White Noise ◽  
Wiener Process ◽  
Stochastic Resonance ◽  
Large Deviation ◽  
Correction Term ◽  
Exit Problem ◽  
Wiener Processes ◽  
Noise Type

Symmetric random walks can be arranged to converge to a Wiener process in the area of normal deviation. However, random walks and Wiener processes have, in general, different asymptotics of the large deviation probabilities. The action functionals for random-walks and Wiener processes are compared in this paper. The correction term is calculated. Exit problem and stochastic resonance for random-walk-type perturbation are also considered and compared with the white-noise-type perturbation.

scholarly journals Differential equations in spaces of Hilbert space valued distributions

2003 ◽  
Vol 68 (3) ◽  
pp. 491-500 ◽  
Author(s):  
Maxim Alshansky
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
White Noise ◽  
Wiener Process ◽  
Gaussian Measure ◽  
Additive Noise ◽  
Covariance Operator ◽  
Operator Coefficient ◽  
White Noise Process ◽  
Tempered Distributions

A Gaussian measure is introduced on the space of Hilbert space valued tempered distributions. It is used to define a Hilbert space valued Q-Wiener process and a white noise process with a nuclear covariance operator Q. The proposed construction is used for solving operator-differential equations with additive noise with the operator coefficient generating an n-times integrated exponentially bounded semigroup.

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