Duality in stochastic processes from the viewpoint of basis expansions. (10th June 2019)

• Record Type: Journal Article
• Authors: Ohkubo, Jun; Arai, Yuuki
• Is Part Of: Journal of statistical mechanics. (2019:Jun.)
• Publication Date: 2019-06-10
• Subjects: 12 -- 15 -- 4; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ab1dd9
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: A new derivation method of duality relations in stochastic processes is proposed. The current focus is on the duality between stochastic differential equations and birth–death processes. Although previous derivation methods have been based on the viewpoint of time-evolution operators, the current derivation is based on basis expansions. In addition, only the tool needed for the derivation is the integration by parts, which is rather simple and understandable. The viewpoint of basis expansions enables us to obtain various dual stochastic processes. As a demonstration, dual processes based on Taylor-type and Hermite polynomials are derived.