@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}
}