2015/08/31 by Hermann Þórisson, Thorisson, Hermann
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Mathematics #Primary 60F15 #Probability (math.PR) #Random Matrices and Applications #Secondary 60G99 #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1508.07838
openalex publication_date 2015/08/31 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
According to the Dudley-Wichura extension of the Skorohod representation\ntheorem, convergence in distribution to a limit in a separable set is\nequivalent to the existence of a coupling with elements converging a.s. in the\nmetric. A density analogue of this theorem says that a sequence of probability\ndensities on a general measurable space has a probability density as a\npointwise lower limit if and only if there exists a coupling with elements\nconverging a.s. in the discrete metric. In this paper the discrete-metric\ntheorem is extended to stochastic processes considered in a widening time\nwindow. The extension is then used to prove the separability version of the\nSkorohod representation theorem.\n