发表机构
New York University, Tandon School of Engineering（纽约大学坦登工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究一类由鞅被积项非线性依赖导致爆炸的奇异BSDE，构造极小解并给出爆炸估计，应用于带状态约束的无限时域随机最优控制，建立验证定理并联系粘性Hamilton-Jacobi方程大解。
AI 中文摘要
我们研究一类至多二次增长的倒向随机微分方程（BSDEs），该类方程在可能无界的随机时域上爆炸，该时域由自适应Ito过程首次击中零点定义。与经典奇异BSDE理论相反，这里的爆炸由生成元对鞅被积项的非线性依赖产生，而非由解分量中的超线性强制性条件产生。我们构造了一个极小奇异解，并推导出其爆炸的双边估计，以及鞅被积项的加权BMO估计。在额外结构假设下，我们还获得了唯一性和精确爆炸速率。对于Hamilton生成元，我们为具有可能非马尔可夫状态约束的无限时域随机最优控制问题建立了验证定理，表明BSDE反馈诱导出唯一的最优受约束律。最后，我们将该理论专门应用于一致椭圆Markov扩散的退出时间，并恢复了与粘性Hamilton-Jacobi方程大解的联系。
英文摘要
We investigate a class of backward stochastic differential equations (BSDEs) with at most quadratic growth which explode at a possibly unbounded random horizon, defined through the first hitting of zero of an adapted Ito process. In contrast with the classical theory of singular BSDEs, the explosion is generated by the nonlinear dependence of the generator on the martingale integrand, rather than by a superlinear coercivity condition in the solution component. We construct a minimal singular solution and derive two-sided estimates on its explosion, together with weighted BMO estimates for the martingale integrand. We also obtain the uniqueness and exact explosion rates under additional structural assumptions. For Hamiltonian generators, we establish a verification theorem for an infinite-horizon stochastic optimal control problem with possible non-Markovian state constraints, showing that the BSDE feedback induces the unique optimal constrained law. We finally specialize the theory to exit times of uniformly elliptic Markov diffusions and recover the connection with large solutions of viscous Hamilton-Jacobi equations.
Comments25 pages ; revised argument for the proof of Theorem 3.9, result unchanged
