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<p>In this paper, we establish the invariance of observability for the observed backward stochastic differential equations (BSDEs) with constant coefficients, relative to the filtered probability space. This signifies that the observability of these observed BSDEs with constant coefficients remains unaffected by the selection of the filtered probability space. As an illustrative application, we demonstrate that for stochastic control systems with constant coefficients, weak observability of the corresponding dual-observation systems, approximate null controllability with cost, and stabilizability are equivalent across some or any filtered probability spaces.</p>

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On Invariance of Observability for BSDEs and Its Applications to Stochastic Control Systems

  • 期刊论文

  • 发表日期：

    2026年6月16日

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  • Bao-Zhu Guo,
  • Huaiqiang Yu,
  • Meixuan Zhang

摘要

In this paper, we establish the invariance of observability for the observed backward stochastic differential equations (BSDEs) with constant coefficients, relative to the filtered probability space. This signifies that the observability of these observed BSDEs with constant coefficients remains unaffected by the selection of the filtered probability space. As an illustrative application, we demonstrate that for stochastic control systems with constant coefficients, weak observability of the corresponding dual-observation systems, approximate null controllability with cost, and stabilizability are equivalent across some or any filtered probability spaces.