论文标题
Feller Square-root过程的首次通行时间问题的累积方法
A cumulant approach for the first-passage-time problem of the Feller square-root process
论文作者
论文摘要
该论文的重点是使用累积物和laguerre-gamma多项式近似的第一个传递时间概率密度函数的近似值。该方法的可行性依赖于从概率密度函数的拉普拉斯变换中恢复的累积和力矩的封闭形式公式，并使用正式功率序列的代数。为了改善近似值，陈述了足够的累积条件。根据符号的微积分，可以使最终的程序更容易实施，并根据偏度，峰度和性高屈肌的合理选择。来自神经元和金融领域的一些案例研究表明，即使在较少的条款方面，近似值也是如此。在论文的末尾解决了开放问题。
The paper focuses on an approximation of the first passage time probability density function of a Feller stochastic process by using cumulants and a Laguerre-Gamma polynomial approximation. The feasibility of the method relies on closed form formulae for cumulants and moments recovered from the Laplace transform of the probability density function and using the algebra of formal power series. To improve the approximation, sufficient conditions on cumulants are stated. The resulting procedure is made easier to implement by the symbolic calculus and a rational choice of the polynomial degree depending on skewness, kurtosis and hyperskewness. Some case-studies coming from neuronal and financial fields show the goodness of the approximation even for a low number of terms. Open problems are addressed at the end of the paper.
