通过布朗桥范围重构的扩散过程精确模拟
Exact Simulation of Diffusions via Brownian Bridge Range Reconstruction
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中文总结 AI 辅助
本文提出一种针对两端无界泊松势的扩散过程精确模拟算法，通过重构布朗桥范围并分解为条件独立桥，实现无时间离散误差的有限维骨架采样，并支持后接受细化。
中文摘要 AI 辅助
我们针对泊松势在两端无界的情形，开发了一种用于标量扩散路径和扩散桥的精确模拟算法。该方法通过采样布朗桥提议的最大值及其位置，以及两个相邻受限布朗游荡的最大值和位置，来重构其实现范围。基于这一有限信息，剩余路径分解为四个条件独立的区间约束布朗桥，这些桥可以在拒绝检验所需的泊松时刻精确采样。与基于包围范围层的构造相比，所提出的表示保留了精确的极值及其位置。我们的算法返回一个无时间离散误差的精确有限维骨架，并允许在任意有限时间集合上进行精确的后接受细化。数值实验验证了所得的有限维分布，并确定受限游荡极值模拟是非线性示例中的主要计算成本。
英文摘要
We develop an exact simulation algorithm for scalar diffusion paths and diffusion bridges when the Poisson potential is unbounded in both tails. The method reconstructs the realized range of a Brownian bridge proposal by sampling its maximum and location, together with the maxima and locations of the two adjacent restricted Brownian meanders. Conditional on this finite information, the remaining path decomposes into four conditionally independent interval-constrained Brownian bridges, which can be sampled exactly at the Poisson times required by the rejection test. In contrast to constructions based on an enclosing range layer, the proposed representation retains the exact extrema and their locations. Our algorithm returns an exact finite-dimensional skeleton without time-discretization error and permits exact post-acceptance refinement at arbitrary finite collections of times. Numerical experiments validate the resulting finite-dimensional laws and identify the restricted-meander extremum simulation as the principal computational cost in the nonlinear example.
