Numerical Density Function and Convergence Analysis
摘要
The density function for the solution of a stochastic differential equation, characterizing all the relevant probabilistic information, is one of the essential characteristics that reveals the probabilistic behavior of the underlying solution. It is of interest to investigate: (1) whether the numerical method can admit the density function when the exact solution is known to possess one, and (2) the error between density functions when both the exact and numerical solutions admit a density function.