On A Notion of Stochastic Zeroing Barrier Function

Tua Agustinus Tamba, Bin Hu, Yul Y. Nazaruddin

Abstract: This paper examines the safety verification of the sample path of Ito's stochastic differential equations (SDE) using a notion of stochastic zeroing barrier function (SZBF). It is shown that an extension of the recently developed zeroing barrier function concept in deterministic systems can be derived to formulate an SZBF based safety verification method for Itó's SDE sample paths. The main tools in the proposed method include Itó's calculus and stochastic invariance concept.