Observability estimate for stochastic Schr?dinger equations [Inégalité d'observabilité pour les équations de Schr?dinger stochastiques]

摘要

In this Note, we present an observability estimate for stochastic Schr?dinger equations with nonsmooth lower order terms. The desired inequality is derived by a global Carleman estimate which is based on a fundamental weighted identity for stochastic Schr?dinger-like operator. As an interesting byproduct, starting from this identity, one can deduce all the known controllability/observability results for several stochastic and deterministic partial differential equations that are derived before via Carleman estimate in the literature.