论文标题
部分可观测时空混沌系统的无模型预测
Multi-Dimensional Super-Linear Backward Stochastic Volterra Integral Equations
论文作者
论文摘要
在本文中，进行了系统的研究，以实现多维向后的随机伏尔泰式积分方程（BSVIE）的一般解决性，而发电机在调整变量$ z $中是超级线性的。讨论了两种主要情况：（i）自由术语与发电机对$ z $的依赖性有界限时``对角线严格''二次增长，并与非双重分子组成相结合； （ii）当自由期限无限制时，具有任意顺序的指数矩，而发电机对$ z $的依赖性在对角线上只不过是二次，并且独立于偏高的组件。此外，对于发电机在$ z $中是超质量的情况，提出了一些负面结果。
In this paper, a systematic investigation is carried out for the general solvability of multi-dimensional backward stochastic Volterra integral equations (BSVIEs) with the generators being super-linear in the adjustment variable $Z$. Two major situations are discussed: (i) When the free term is bounded with the dependence of the generator on $Z$ being of ``diagonally strictly'' quadratic growth and being sub-quadratically coupled with off-diagonal components; (ii) When the free term is unbounded having exponential moments of arbitrary order with the dependence of the generator on $Z$ being diagonally no more than quadratic and being independent of off-diagonal components. Besides, for the case that the generator is super-quadratic in $Z$, some negative results are presented.
