We construct a fast exact algorithm for the simulation of the first-passage time, jointly with the undershoot and overshoot, of a tempered stable subordinator over an arbitrary non-increasing absolutely continuous function. We prove that the running time of our algorithm has finite exponential moments and provide bounds on its expected running time with explicit dependence on the characteristics of the process and the initial value of the function. The expected running time grows at most cubically in the stability parameter (as it approaches either $0$ or $1$) and is linear in the tempering parameter and the initial value of the function. Numerical performance, based on the implementation in the dedicated GitHub repository, exhibits a good agreement with our theoretical bounds. We provide numerical examples to illustrate the performance of our algorithm in Monte Carlo estimation.

翻译：我们针对经过调和的稳定子跨越任意非增绝对连续函数首次通过时间（联合下冲与上冲）构建了一种快速精确模拟算法。我们证明了该算法的运行时间具有有限指数矩，并给出了其期望运行时间关于过程特征与函数初始值的显式依赖界。期望运行时间关于稳定性参数（当其趋近0或1时）至多呈三次增长，关于调和参数与函数初始值呈线性增长。基于专用GitHub仓库实现的数值性能与理论界高度吻合。我们提供数值示例以展示该算法在蒙特卡洛估计中的性能。