Convergence Theory of a Numerical Method for Solving the Chapman--Kolmogorov Equation
Yuzhi Cai · SIAM Journal on Numerical Analysis · 2002
A convergence theory has been established for a new numerical method for solving the Chapman--Kolmogorov equation [Y. Cai, A Numerical Forecasting Procedure for Nonlinear Autoregressive Time Series Model, manuscript, Department of Mathematics and Statistics, University of Surrey, Surrey, UK, 2001]. The theory has been applied to many types of nonlinear time series models in order to obtain m-step ahead predictive probability density function, predictive cumulative distribution function, predictive mean, and predictive variance.