@Article{duepublico_mods_00005251, author = {Landers, D. and Rogge Prof. Dr., Lothar}, title = {Nonstandard Characterization of Convergence in Law for D[0,1]-Valued Random Variables}, year = {2012}, month = {Jul}, day = {03}, keywords = {Nonstandard Characterization; 28E05 Nonstandard measure theory; 60B12 Limit theorems for vector-valued random vari; Convergence in law for processes}, abstract = {We prove for random variables with values in the space D[0,1] of cadlag functions - endowed with the supremum metric - that convergence in law is equivalent to nonstandard constructions of internal S-cadlag processes, which represent up to an infinitesimal error the limit process. It is not required that the limit process is concentrated on the space C[0,1], so that the theory is applicable to a wider class of limit processes as e.g. to Poisson processes or Gaussian processes. If we consider in D[0,1] the Skorokhod metric - instead of the supremum metric - we obtain a corresponding equivalence to constructions of internal processes with S-separated jumps. We apply these results to functional central limit theorems.}, url = {https://duepublico2.uni-due.de/receive/duepublico_mods_00005251}, file = {:https://duepublico2.uni-due.de/servlets/MCRFileNodeServlet/duepublico_derivate_00005251/mathe141998.pdf:PDF}, language = {en} }