Nonstandard Representation of the Dirichlet Form

Autor:	Anderson, Robert M., Duanmu, Haosui, Smith, Aaron
Rok vydání:	2020
Předmět:	Mathematics - Probability Mathematics - Logic 60J05 (primary) 28E05 26E35
Druh dokumentu:	Working Paper
Popis:	The Dirichlet form is a generalization of the Laplacian, heavily used in the study of many diffusion-like processes. In this paper we present a nonstandard representation theorem for the Dirichlet form, showing that the usual Dirichlet form can be well-approximated by a hyperfinite sum. One of the main motivations for such a result is to provide a tool for directly translating results about Dirichlet forms on finite or countable state spaces to results on more general state spaces, without having to translate the details of the proofs. As an application, we prove a generalization of a well-known comparison theorem for Markov chains on finite state spaces, and also relate our results to previous generalization attempts. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2010.02452 Zobrazit plný text záznamu View this record from Arxiv