scholarly journals Large Deviation Principle for a Stochastic Heat Equation With Spatially Correlated Noise

2003 ◽  
Vol 8 (0) ◽  
Author(s):  
David Marquez-Carreras ◽  
Monica Sarra
Keyword(s):  
Heat Equation ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stochastic Heat Equation ◽  
Correlated Noise ◽  
Spatially Correlated ◽  
Deviation Principle ◽  
Spatially Correlated Noise

scholarly journals Moderate deviations for a fractional stochastic heat equation with spatially correlated noise

2017 ◽  
Vol 17 (04) ◽  
pp. 1750025 ◽  
Author(s):  
Yumeng Li ◽  
Ran Wang ◽  
Nian Yao ◽  
Shuguang Zhang
Keyword(s):  
Heat Equation ◽  
Moderate Deviation ◽  
Stochastic Heat Equation ◽  
Correlated Noise ◽  
Derivative Operator ◽  
Spatially Correlated ◽  
Whole Space ◽  
Convergence Method ◽  
Spatially Correlated Noise ◽  
Weak Convergence Method

In this paper, we study the Moderate Deviation Principle for a perturbed stochastic heat equation in the whole space [Formula: see text]. This equation is driven by a Gaussian noise, white in time and correlated in space, and the differential operator is a fractional derivative operator. The weak convergence method plays an important role.

Large deviation principle for a space-time fractional stochastic heat equation with fractional noise

2018 ◽  
Vol 21 (2) ◽  
pp. 462-485 ◽  
Author(s):  
Litan Yan ◽  
Xiuwei Yin
Keyword(s):  
Heat Equation ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Fractional Integration ◽  
Fractional Power ◽  
Space Time ◽  
Stochastic Heat Equation ◽  
Fractional Noise ◽  
Deviation Principle ◽  
Fractional Integration Operator

Abstract In this paper, we consider the large deviation principle for a class of space-time fractional stochastic heat equation $$\begin{array}{} \displaystyle \partial^\beta_tu^\varepsilon(t,x)=-\nu(-\Delta)^{\frac\alpha 2}u^\varepsilon(t,x)+I_t^{1-\beta}f(u^\varepsilon(t,x))+ \sqrt{\varepsilon}I^{1-\beta}_t[\dot{W}^H(t,x)], \end{array}$$ where ẆH is a fractional white noise, ν > 0, β ∈ (0, 1), α ∈ (0, 2]. The operator $\begin{array}{} \displaystyle \partial^\beta_t \end{array}$ is the Caputo fractional integration operator, and $\begin{array}{} \displaystyle -(-\Delta)^{\frac\alpha 2} \end{array}$ is the fractional power of Laplacian. Our proof is based on the weak convergence approach.

AUTOMATIC ESTIMATION OF SPATIALLY CORRELATED NOISE VARIANCE IN SPECTRAL DOMAIN FOR IMAGES

2014 ◽  
Vol 73 (6) ◽  
pp. 511-527 ◽  
Author(s):  
V.V. Abramova ◽  
S. K. Abramov ◽  
V. V. Lukin ◽  
A. A. Roenko ◽  
Benoit Vozel
Keyword(s):  
Spectral Domain ◽  
Correlated Noise ◽  
Noise Variance ◽  
Spatially Correlated ◽  
Automatic Estimation ◽  
Spatially Correlated Noise

Large deviation principle for the field in prequantum classical statistical field theory

2017 ◽  
Vol 20 (04) ◽  
pp. 1750025
Author(s):  
Andrei Khrennikov ◽  
Achref Majid
Keyword(s):  
Field Theory ◽  
Random Field ◽  
Field Model ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Background Field ◽  
Deviation Principle ◽  
Statistical Field ◽  
Statistical Field Theory

In this paper, we prove a large deviation principle for the background field in prequantum statistical field model. We show a number of examples by choosing a specific random field in our model.

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