论文标题
部分可观测时空混沌系统的无模型预测
Approximating the first passage time density from data using generalized Laguerre polynomials
论文作者
论文摘要
本文分析了一种近似第一个传递时间概率密度函数的方法，如果只有样本数据可用，该方法将特别有用。该方法依赖于laguerre-gamma多项式近似，并且迭代地寻找最佳的多项式程度，因此拟合函数是概率密度函数。提出的迭代算法依赖于涉及第一通道时间矩的简单和新的递归公式。如果已知的话，可以从累积物中递归计算这些时刻。在这种情况下，近似密度也可以用于基础随机过程参数的最大似然估计。如果未知累积物，则采用依赖K统计量的合适无偏估计量。为了检查该方法在拟合密度和估计参数时的可行性，考虑了几何布朗运动的第一个传递时间问题。
This paper analyzes a method to approximate the first passage time probability density function which turns to be particularly useful if only sample data are available. The method relies on a Laguerre-Gamma polynomial approximation and iteratively looks for the best degree of the polynomial such that the fitting function is a probability density function. The proposed iterative algorithm relies on simple and new recursion formulae involving first passage time moments. These moments can be computed recursively from cumulants, if they are known. In such a case, the approximated density can be used also for the maximum likelihood estimates of the parameters of the underlying stochastic process. If cumulants are not known, suitable unbiased estimators relying on k-statistics are employed. To check the feasibility of the method both in fitting the density and in estimating the parameters, the first passage time problem of a geometric Brownian motion is considered.
