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Large Deviation Principle of Stochastic Evolution Equations with reflection

Zdzisław Brzeźniak, Qi Li, Tusheng Zhang

Abstract

In this paper, we establish a large deviation principle for stochastic evolution equations with reflection in an infinite dimensional ball. Weak convergence approach plays an important role.

Large Deviation Principle of Stochastic Evolution Equations with reflection

Abstract

In this paper, we establish a large deviation principle for stochastic evolution equations with reflection in an infinite dimensional ball. Weak convergence approach plays an important role.
Paper Structure (6 sections, 9 theorems, 103 equations)

This paper contains 6 sections, 9 theorems, 103 equations.

Table of Contents

  1. Introduction
  2. Framework
  3. A sufficient Condition for LDP
  4. Skeleton Equations
  5. Large Deviations
  6. LDP of Reflected Stochastic Navier Stokes Equations

Key Result

Theorem 2.1

Let the assumptions (A.1)-(A.3) hold. The reflected stochastic evolution equation(SEE) admits a unique solution $(u,L)$ that satisfies, for $T>0$,

Theorems & Definitions (16)

  • Definition 2.1
  • Theorem 2.1
  • Definition 3.1
  • Definition 3.2
  • Theorem 3.1
  • Proposition 4.1
  • proof
  • Theorem 4.1
  • proof
  • Proposition 4.2
  • ...and 6 more