Moderate Deviations for a Stochastic Schr\"odinger Equation with Linear Drift

TL;DR

This paper establishes moderate deviation principles and a central limit theorem for a stochastic Schr"odinger equation with linear drift and Q-Wiener noise, advancing understanding of its asymptotic behavior.

Contribution

It introduces the first moderate deviation principle for this class of stochastic Schr"odinger equations using the weak convergence approach.

Findings

Moderate deviation principle proven for the equation.

Central limit theorem established for the stochastic Schr"odinger equation.

Enhanced understanding of the asymptotic behavior of solutions.

Abstract

Moderate deviation principle is achieved by the weak convergence approach for a stochastic Schr\"odinger type equation with linear drift term and noise driven by a $Q$-Wiener process. The central limit theorem is also shown for the equation to further analyze its asymptotic behavior.