A cumulant approach for the first-passage-time problem of the Feller square-root process
作者：
Highlights：
• Closed form expressions for cumulants and moments of any order of the first passage time of the square root (CIR) stochastic process through a constant boundary, using the algebra of formal power series.
• Approximation of the first passage time probability density function of a CIR stochastic process by using cumulants and Laguerre-Gamma polynomials.
• Sufficient conditions on cumulants for the goodness of the approximation.
• Case studies from neuronal and financial models.
摘要
•Closed form expressions for cumulants and moments of any order of the first passage time of the square root (CIR) stochastic process through a constant boundary, using the algebra of formal power series.•Approximation of the first passage time probability density function of a CIR stochastic process by using cumulants and Laguerre-Gamma polynomials.•Sufficient conditions on cumulants for the goodness of the approximation.•Case studies from neuronal and financial models.
论文关键词：Hitting times,CIR model,Laguerre series,Formal power series,Symbolic calculus
论文评审过程：Received 31 March 2020, Revised 22 April 2020, Accepted 20 September 2020, Available online 6 October 2020, Version of Record 6 October 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125707
