半线性 PDEs 和 BSDEs 的分层回归 Monte-Carlo 方案及其在 GPU 上的大规模并行化
Stratified regression Monte-Carlo scheme for semilinear PDEs and BSDEs with large scale parallelization on GPUs
AI总结：
本文提出一种基于 LSMC 的新算法求解离散时间 BSDEs，通过引入新颖的分层方法实现 GPU 大规模并行计算，有效降低了模拟存储的内存开销。
摘要：
本文设计了一种基于 Least-Squares Monte Carlo (LSMC) 的新算法，用于近似求解离散时间 Backward Stochastic Differential Equations (BSDEs) 的解。该算法允许在图形处理器 (GPUs) 等多核处理器上进行大规模并行计算。该方法包含一种新颖的分层方法，这对于大规模并行化至关重要。通过这种方式，我们最小化了因存储模拟而产生的内存需求。实际上，我们注意到该方法与先前工作相比具有更低的内存开销。
英文摘要：
In this paper, we design a novel algorithm based on Least-Squares Monte Carlo (LSMC) in order to approximate the solution of discrete time Backward Stochastic Differential Equations (BSDEs). Our algorithm allows massive parallelization of the computations on many core processors such as graphics processing units (GPUs). Our approach consists of a novel method of stratification which appears to be crucial for large scale parallelization. In this way, we minimize the exposure to the memory requirements due to the storage of simulations. Indeed, we note the lower memory overhead of the method compared with previous works.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
