Diffusion Simulation via Green Function Evaluation

Abstract

In the present paper, a scheme of path sampling is explored for stochastic diffusion processes. The core issue is the evaluation of the diffusion propagators (spatial–temporal Green functions) by solving the corresponding Kolmogorov forward equations with Dirac delta functions as initials. The technique can be further used in evaluating general functional of path integrals. The numerical experiments demonstrated that the simulation scheme based on this approach overwhelms the popular Euler scheme and Exact Algorithm in terms of accuracy and efficiency in fairly general settings. An example of likelihood inference for the diffusion driven Cox process is provided to show the scheme’s potential power in applications.

Keywords

Cox process / Kolmogorov forward equation / Killing diffusion process / Stochastic diffusion process / Sample path simulation / Monte Carlo calculation