The Law of Iterated Logarithm for a Linear Stochastic Schrodinger Equation

TL;DR

This paper establishes a law of the iterated logarithm for a stochastic Schrödinger equation using moderate deviation principles and classical probabilistic methods.

Contribution

It introduces a novel application of the Azencott method to derive the Strassen's law for stochastic Schrödinger equations.

Findings

Proves the Strassen's law of the iterated logarithm for the equation.

Utilizes the Friedlin-Wentzell inequality in the proof.

Establishes a connection between moderate deviations and the law of the iterated logarithm.

Abstract

The moderate deviation principle is achieved for a stochastic Schrodinger type equation by applying the classical Azencott method. The Friedlin-Wentzell inequality derived by this method is then used to prove the Strassen's compact law of the iterated logarithm for the equation.