2006/01/22 by Jean C. Cortissoz, Jean Cortissoz, Cortissoz, Jean
Computer Science · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Rough Sets and Fuzzy Logic #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.math/0601524
arxiv created 2006/01/22 · openalex publication_date 2006/01/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we present a variant of the well known Skorokhod Representation Theorem. In our main result, given S a Polish space, to a given continous path α in the space of probability measures on S, we associate a continuous path in the space of S-valued random variables on a nonatomic probability space (endowed with the topology of the convergence in probability). We call this associated path a lifting of α. an interesting feature of our result is that we can fix the endpoints ("boundary values") of the lifting of α, as long as their distribution correspond to the endpoints ("boundary values") of α. We also discuss an n-dimensional generalization of this result.