Estimating parameters of stochastic differential equations using a criterion function based on the Kolmogorov-Smirnov statistics

Abstract

We introduce a method for the estimation of stochastic differential equation coefficients from panel data. The method involves matching the distribution of the experimental/field data with a panel of simulated data generated by a Monte Carlo experiment. The fit between the two distributions is assessed by means of Kolmogorov-Smirnov goodness-of-fit statistic leading to a confidence function computed from an incomplete gamma function. A numerical optimization algorithm then optimizes the choice of parameters to maximize this function.