Constrained Brownian processes and constrained Brownian bridges. (3rd February 2017)

• Record Type: Journal Article
• Authors: Mazzolo, Alain
• Is Part Of: Journal of statistical mechanics. (2017:Feb.)
• Publication Date: 2017-02-03
• Subjects: 4 -- 15; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aa4f15
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We present a novel approach to describe Brownian paths that end at a given final point at a fixed time, and having the additional constrain of a fixed area under its curve. Both anticipative (in this case, knowledge of the future of the path is required) and non-anticipative solutions are exposed. In particular, for the non-anticipative representation a local stochastic differential equation is derived which leads to an effective Langevin equation. This representation allows us to generate statistically independent realizations of the constrained process in a very efficient way.