scholarly journals Large deviation principle for stochastic heat equation with memory

2015 ◽  
Vol 35 (11) ◽  
pp. 5221-5237 ◽  
Author(s):  
Yueling Li ◽  
◽  
Yingchao Xie ◽  
Xicheng Zhang ◽  
Keyword(s):  
Heat Equation ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stochastic Heat Equation ◽  
Deviation Principle ◽  
Heat Equation With Memory ◽  
With Memory

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.

scholarly journals Optimal control for stochastic heat equation with memory

2014 ◽  
Vol 3 (1) ◽  
pp. 35-58 ◽  
Author(s):  
Fulvia Confortola ◽  
◽  
Elisa Mastrogiacomo ◽  
Keyword(s):  
Optimal Control ◽  
Heat Equation ◽  
Stochastic Heat Equation ◽  
Heat Equation With Memory ◽  
With Memory

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.

Dynamic behavior of a heat equation with memory

2009 ◽  
Vol 32 (10) ◽  
pp. 1287-1310 ◽  
Author(s):  
Jun-Min Wang ◽  
Bao-Zhu Guo ◽  
Meng-Yin Fu
Keyword(s):  
Heat Equation ◽  
Dynamic Behavior ◽  
Heat Equation With Memory ◽  
With Memory

scholarly journals LARGE DEVIATIONS FOR FLOWS OF INTERACTING BROWNIAN MOTIONS

2010 ◽  
Vol 10 (03) ◽  
pp. 315-339 ◽  
Author(s):  
A. A. DOROGOVTSEV ◽  
O. V. OSTAPENKO
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stochastic Flows ◽  
Brownian Motions ◽  
Deviation Principle ◽  
And Brownian Motion

We establish the large deviation principle (LDP) for stochastic flows of interacting Brownian motions. In particular, we consider smoothly correlated flows, coalescing flows and Brownian motion stopped at a hitting moment.

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