A large deviations principle for small perturbations of random evolution equation in Hölder norm

1999 ◽  
Vol 4 (1) ◽  
pp. 4-4
Author(s):  
Jin Wenze ◽  
Liu Jingjun ◽  
Hu Yijun
Keyword(s):  
Evolution Equation ◽  
Large Deviations ◽  
Random Evolution ◽  
Large Deviations Principle ◽  
Small Perturbations ◽  
Hölder Norm

Large deviations for random evolution equation in Besov-Orlicz space

2020 ◽  
pp. 357-387
Author(s):  
Dina Miora Rakotonirina ◽  
Jocelyn Hajaniaina Andriatahina ◽  
Rado Abraham Randrianomenjanahary ◽  
Toussaint Joseph Rabeherimanana
Keyword(s):  
Evolution Equation ◽  
Large Deviations ◽  
Orlicz Space ◽  
Evolution Equations ◽  
Random Evolution ◽  
Young Function ◽  
Large Deviations Principle

In this paper, we develop a large deviations principle for random evolution equations to the Besov-Orlicz space $\mathcal{B}_{M_2, w}^{v, 0}$ corresponding to the Young function $M_2(x)=\exp(x^2)-1$.

scholarly journals On Jumps Stochastic Evolution Equations With Application of Homogenization and Large Deviations

2019 ◽  
Vol 11 (2) ◽  
pp. 125
Author(s):  
Cl´ement Manga ◽  
Alioune Coulibaly ◽  
Alassane Diedhiou
Keyword(s):  
Evolution Equation ◽  
Large Deviations ◽  
Evolution Equations ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Large Deviations Principle ◽  
Viscosity Parameter ◽  
Two Parameters ◽  
And Diffusion

We consider a class of jumps and diffusion stochastic differential equations which are perturbed by to two parameters:  ε (viscosity parameter) and δ (homogenization parameter) both tending to zero. We analyse the problem taking into account the combinatorial effects of the two parameters  ε and δ . We prove a Large Deviations Principle estimate for jumps stochastic evolution equation in case that homogenization dominates.

scholarly journals Large deviations for a stochastic Cahn–Hilliard equation in Hölder norm

2020 ◽  
Vol 23 (02) ◽  
pp. 2050010
Author(s):  
Lahcen Boulanba ◽  
Mohamed Mellouk
Keyword(s):  
Weak Convergence ◽  
Large Deviations ◽  
White Noise ◽  
Space Time ◽  
Large Deviations Principle ◽  
Hilliard Equation ◽  
Hölder Norm ◽  
The Law ◽  
Cahn Hilliard Equation ◽  
Weak Convergence Approach

We consider a stochastic Cahn–Hilliard equation driven by a space–time white noise. We prove that the law of the solution satisfies a large deviations principle in the Hölder norm. Our proof is based on the weak convergence approach for large deviations.

scholarly journals Run-and-Tumble Motion: The Role of Reversibility

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Bart van Ginkel ◽  
Bart van Gisbergen ◽  
Frank Redig
Keyword(s):  
Free Energy ◽  
Diffusion Coefficient ◽  
Large Deviations ◽  
Energy Function ◽  
Internal State ◽  
Rate Function ◽  
Free Energy Function ◽  
Large Deviations Principle ◽  
Preferred Direction ◽  
State Process

AbstractWe study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier–Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples.

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