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<p>This study focuses on generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. Firstly, we establish the large deviation principle for forward stochastic differential equations with reflecting boundaries under weak monotonicity conditions. Subsequently, by utilizing the obtained result and applying the contraction principle, we prove the large deviation principle for the generalized backward stochastic differential equations. Additionally, as a supplementary outcome, we derive a limiting result concerning second order parabolic partial differential equations with nonlinear Neumann boundary conditions.</p>

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Large Deviations for Generalized Backward Stochastic Differential Equations

  • 期刊论文

  • 发表日期：

    2026年3月21日

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  • Yawen Liu,
  • Huijie Qiao

摘要

This study focuses on generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. Firstly, we establish the large deviation principle for forward stochastic differential equations with reflecting boundaries under weak monotonicity conditions. Subsequently, by utilizing the obtained result and applying the contraction principle, we prove the large deviation principle for the generalized backward stochastic differential equations. Additionally, as a supplementary outcome, we derive a limiting result concerning second order parabolic partial differential equations with nonlinear Neumann boundary conditions.