scholarly journals Large Deviation Principle for McKean–Vlasov Quasilinear Stochastic Evolution Equations

2021 ◽  
Author(s):  
Wei Hong ◽  
Shihu Li ◽  
Wei Liu
Keyword(s):  
Evolution Equations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Deviation Principle

Large deviation principle for semilinear stochastic evolution equations with Poisson noise

2017 ◽  
Vol 20 (02) ◽  
pp. 1750009
Author(s):  
Hassan Dadashi
Keyword(s):  
Evolution Equations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Functional Differential Equations ◽  
Random Measure ◽  
Poisson Noise ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Deviation Principle ◽  
Wide Range

We demonstrate the large deviation principle in the small noise limit for the mild solution of semilinear stochastic evolution equations with monotone nonlinearity and multiplicative Poisson noise. A recently developed method in studying the large deviation principle, weak convergent method, is employed. We apply the result obtained by Budhiraja et al.,7 that reveals the variational representation of exponential integrals w.r.t. the Poisson random measure. Our framework covers a wide range of parabolic, hyperbolic and functional differential equations. We give some examples to illustrate the applications of our results.

scholarly journals Smoothness of solutions of stochastic evolution equations and the existence of a filtering transition density

1981 ◽  
Vol 84 ◽  
pp. 195-208 ◽  
Author(s):  
B. L. Rozovskii ◽  
A. Shimizu
Keyword(s):  
Evolution Equations ◽  
Transition Density ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Smoothness Of Solutions

In this paper, we shall discuss the smoothness of solutions of stochastic evolution equations, which has been investigated in N. V. Krylov and B. L. Rozovskii [2] [3], to establish the existence of a filtering transition density.

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.

scholarly journals On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Banach Fixed Point Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Composition Theorem

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

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