Observability Estimate for Stochastic Schroedinger Equations

TL;DR

This paper develops a boundary observability estimate for stochastic Schrödinger equations using a novel Carleman estimate based on a new fundamental identity, with applications to state observation and unique continuation problems.

Contribution

It introduces a new fundamental identity and a Carleman estimate for stochastic Schrödinger equations, advancing the analysis of observability and unique continuation.

Findings

Established boundary observability estimate for stochastic Schrödinger equations

Applied the estimate to state observation problems

Addressed the unique continuation problem for stochastic Schrödinger equations

Abstract

In this paper, we establish a boundary observability estimate for stochastic Schr\"{o}dinger equations by means of the global Carleman estimate. Our Carleman estimate is based on a new fundamental identity for a stochastic Schr\"{o}dinger-like operator. Applications to the state observation problem for semilinear stochastic Schr\"{o}dinger equations and the unique continuation problem for stochastic Schr\"{o}dinger equations are also addressed.