{"title":"Diffusion Simulation via Green Function Evaluation","authors":"Lin Sun, Shuaishuai Chen, Gang Wei","doi":"10.1007/s40304-023-00384-0","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40304-023-00384-0","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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