BACKWARD MARTINGALE TRANSPORT AND FITZPATRICK FUNCTIONS IN PSEUDO-EUCLIDEAN SPACES

• 成果类型: Article
• 署名作者: Kramkov, Dmitry; Sirbu, Mihai
• 署名单位: Carnegie Mellon University; University of Texas System; University of Texas Austin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1998
• 发表日期: 2024
• 页码: 1571-1599
• 关键词: positive sets

摘要

We study an optimal transport problem with a backward martingale constraint in a pseudo-Euclidean space S. We show that the dual problem consists in the minimization of the expected values of the Fitzpatrick functions associated with maximal S-monotone sets. An optimal plan. and an optimal maximal S-monotone set G are characterized by the condition that the support of. is contained in the graph of the S-projection on G. For a Gaussian random variable Y, we get a unique decomposition: Y = X+ Z, where X and Z are independent Gaussian random variables taking values, respectively, in complementary positive and negative linear subspaces of the S-space.