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Diffusion Simulation via Green Function Evaluation

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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.

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Notes

  1. An R language package providing an interface between R and the C++ matrix calculation package Armadillo.

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Authors and Affiliations

  1. Zhongtai Securities Institute for Financial Studies, Shandong University, 27 Shandananlu, Jinan, 250100, People’s Republic of China

    Lin Sun

  2. School of Mathematics, Shandong University, 27 Shandananlu, Jinan, 250100, People’s Republic of China

    Shuaishuai Chen & Gang Wei

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  1. Lin Sun
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  2. Shuaishuai Chen
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  3. Gang Wei
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Correspondence to Gang Wei.

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Sun, L., Chen, S. & Wei, G. Diffusion Simulation via Green Function Evaluation. Commun. Math. Stat. (2024). https://doi.org/10.1007/s40304-023-00384-0

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