论文标题
Ornstein-Uhlenbeck过程的分析生存分析
Analytical Survival Analysis of the Ornstein-Uhlenbeck Process
论文作者
论文摘要
我们使用从微分方程理论中使用渐近方法来获得分析表达，以实现Ornstein-Uhlenbeck过程的生存概率，其潜力在广泛的域上定义。我们通过在内部区域中渐近匹配围绕原点的内部区域中的近似近似解决方案，形成了覆盖整个域的均匀连续分析溶液，与边界层中的那些近似，靠近域的横向边界。分析解决方案与数值解决方案非常吻合，并考虑了在随机过程开始接近一个边界时短时间发生的概率的不可忽略的泄漏。鉴于Ornstein-Uhlenbeck过程的应用范围，分析解决方案在许多自然和工程科学领域都具有广泛的相关性。
We use asymptotic methods from the theory of differential equations to obtain an analytical expression for the survival probability of an Ornstein-Uhlenbeck process with a potential defined over a broad domain. We form a uniformly continuous analytical solution covering the entire domain by asymptotically matching approximate solutions in an interior region, centered around the origin, to those in boundary layers, near the lateral boundaries of the domain. The analytic solution agrees extremely well with the numerical solution and takes into account the non-negligible leakage of probability that occurs at short times when the stochastic process begins close to one of the boundaries. Given the range of applications of Ornstein-Uhlenbeck processes, the analytic solution is of broad relevance across many fields of natural and engineering science.
