非自治Ornstein-Uhlenbeck过程的解析生存分析
Analytical Survival Analysis of the Non-autonomous Ornstein-Uhlenbeck Process
AI总结：
针对周期性非自治Ornstein-Uhlenbeck过程的生存概率计算问题，提出渐近匹配法与积分关系法两种解析求解方案，经数值验证渐近方法的解有效性更优。
摘要：
本文采用两种不同方法解析计算了周期性非自治Ornstein-Uhlenbeck过程的生存概率。第一种方法采用渐近分析思路：针对带吸收边界的关联Kolmogorov向后方程（柯尔莫哥洛夫向后方程），将求解域划分为以原点为中心的内部区域和吸收边界附近的“边界层”，分别求解各区域的首阶解析解，再通过渐近匹配构造全域一致有效的解。第二种方法探究概率密度函数与平均首次通过时间概率密度函数之间的积分关系，以此推导退出率的近似解析形式。通过数值评估两种方法所得解的有效性，结果表明渐近方法性能更优。
英文摘要：
The survival probability for a periodic non-autonomous Ornstein-Uhlenbeck process is calculated analytically using two different methods. The first uses an asymptotic approach. We treat the associated Kolmogorov Backward Equation with an absorbing boundary by dividing the domain into an interior region, centered around the origin, and a "boundary layer" near the absorbing boundary. In each region we determine the leading-order analytical solutions, and construct a uniformly valid solution over the entire domain using asymptotic matching. In the second method we examine the integral relationship between the probability density function and the mean first passage time probability density function. These allow us to determine approximate analytical forms for the exit rate. The validity of the solutions derived from both methods is assessed numerically, and we find the asymptotic method to be superior.
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。
