ON CONTIGUITY, ENTIRE SEPARATION AND CONVERGENCE IN VARIATION OF SEQUENCES OF MEASURES INDURESINDUCED BY STOCHASTIC RROCESSES

By using the necessary and sufficient conditions for entire separation and convergence in variation of sequences of probability measures given in terms of Kakutani’s distance between probability measures, with respect to probability measures sequences induced by Gaussian processes and stochastically continuous processes with independent increments the necessary and sufficient conditions for the contiguty, entire separation and convergence in variation are shown.The conclusions about Gaussian processes are more complete than that in 4.With respect to processes with independent increments our calculations of Kakutani’s distance are simpler than that in 8, because we use the explicit forms of derivatives of measures induced by processes with independent increments.