发表机构
Stanford University（斯坦福大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对系数有界的多元扩散过程及桥过程，提出了首个有限期望成本的通用精确采样算法，结合随机参数化展开与有限加权图，实现了极小极大最优采样。
AI 中文摘要
我们提供了首个具有有限期望总成本的通用精确采样算法，适用于系数有界且一阶导数连续有界的一致椭圆型多元扩散过程及对应的扩散桥过程。我们构建了一个计算成本模型，该模型通过统计生成高斯随机变量和均匀随机变量以执行接受-拒绝采样的工作量，以及漂移项和扩散项系数的函数评估，还有求和、乘法等基本操作来衡量成本。我们的构造结合了随机参数化展开与包含桥过程两端点的有限加权图，用于生成提议样本。该扩散过程的精确采样在时间跨度与请求观测数量上联合达到极小极大最优，而桥过程采样在固定时间跨度和端点的条件下，于观测数量上达到极小极大最优。
英文摘要
We provide the first generic exact sampling algorithms with finite expected total cost for uniformly elliptic multivariate diffusions and the corresponding diffusion bridges with bounded coefficients and bounded continuous first derivatives. We formulate a computational cost model that counts work in terms of generation of Gaussian and uniform random variables to execute acceptance--rejection sampling, as well as function evaluations of the drift and diffusion coefficients, together with elementary operations such as sums and multiplications. Our constructions combine randomized parametrix expansions with a finite weighted graph that incorporates both bridge endpoints into the proposal. The exact sampling of the diffusion is minimax optimal jointly in the horizon and number of requested observations, while bridge sampling is minimax optimal in the number of observations for fixed horizon and endpoints.
