发表机构
Simion Stoilow Institute of Mathematics of the Romanian Academy; Faculty of Mathematics, ”Alexandru Ioan Cuza” University of Iaşi; Octav Mayer Institute of Mathematics of the Romanian Academy, Iaşi branch（罗马尼亚科学院西奥多·斯托伊洛数学研究所; 雅西亚历山德鲁·乔安·库扎大学数学学院; 罗马尼亚科学院奥克塔夫·梅耶数学研究所雅西分部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在一般完备过滤空间上，通过构造对称两点核克服非对称旋转场带来的切向项，证明了平面斜反射倒向随机变分不等式强càdlàg解的存在唯一性，并建立了相关最优控制问题。
AI 中文摘要
我们在一个一般完备过滤概率空间上，证明了由平方可积鞅（可能具有跳跃）驱动的平面倒向随机变分不等式存在唯一一个càdlàg解。多值项是某个有界一致凸平面区域的外法锥算子，反射方向由依赖于时间的非对称旋转场生成。非对称性产生了一个一阶切向边界项，破坏了对称斜反射理论中使用的标准单调性和二次压缩估计。我们通过构造一个具有状态依赖系数的显式对称两点核来克服这一障碍，该核的边界导数抵消了主要的切向贡献。随后，一个加权鞅指数估计控制了二阶缺陷和跳跃项。在适当的几何和定量相容性约束下，我们获得了唯一的强càdlàg解。我们还为旋转角制定了相关的控制问题，并证明了在一类有界速率的角路径的紧类中存在最优控制。
英文摘要
We prove existence and uniqueness of a càdlàg solution to a planar backward stochastic variational inequality on a general complete filtered probability space, driven by a square integrable martingale, which may have jumps. The multivalued term is the exterior normal cone operator of a bounded uniformly convex planar domain, and the reflection direction is generated by a time-dependent non-symmetric rotation field. The non-symmetry creates a first-order tangential boundary term that destroys the standard monotonicity and quadratic contraction estimates, used in the symmetric oblique-reflection theory. We overcome this obstruction by constructing an explicit symmetric two-point kernel with state dependent coefficients, whose boundary derivative cancels the leading tangential contribution. A weighted martingale-exponential estimate then controls the second order defect and the jump terms. Under suitable geometric and quantitative compatibility constraints, we obtain the unique strong càdlàg solution. We also formulate associated control problems for the rotation angle and prove existence of an optimal control in a compact class of bounded-rate angle paths.
Comments45 pages
