论文标题
矩阵值的随机指数和对二次BSDE系统的应用的反向Hölder不等式
The reverse Hölder inequality for matrix-valued stochastic exponentials and applications to quadratic BSDE systems
论文作者
论文摘要
在本文中，我们研究了三个概念之间的联系 - 矩阵值的矩阵的反向Hölder不平等，带有无限系数的线性BSDE的适当性，以及Quadratic BSDE系统的良好性。特别是，我们表明，当且仅当相关矩阵值的Martingale的随机指数满足反向Hölder的不平等时，且仅当具有BMO（有界平均振荡）系数的线性BSDE才能得到充分范围。此外，我们提供了满足这两个等效条件的结构条件。最后，我们将结果应用于线性方程式，以获得具有特殊结构的两种新类的非马克维亚二次二次BSDE系统的全球适应性结果。
In this paper, we study the connections between three concepts - the reverse Hölder inequality for matrix-valued martingales, the well-posedness of linear BSDEs with unbounded coefficients, and the well-posedness of quadratic BSDE systems. In particular, we show that a linear BSDE with bmo (bounded mean oscillation) coefficients is well-posed if and only if the stochastic exponential of a related matrix-valued martingale satisfies a reverse Hölder inequality. Furthermore, we give structural conditions under which these two equivalent conditions are satisfied. Finally, we apply our results on linear equations to obtain global well-posedness results for two new classes of non-Markovian quadratic BSDE systems with special structure.
