Abstract:
The basic result in this paper (Theorem 1) generalizes the well-known criterion of Kakutani to measures corresponding to arbitrary random sequences. The proof is based on Theorem 6, which gives a description of the set of convergence of a submartingale with bounded increments. The question of absolute continuity and singularity of measures corresponding to solutions of stochastic difference equations is studied. The dichotomy for Gaussian measures is obtained as a corollary.
Bibliography: 13 titles.
Citation:
Yu. M. Kabanov, R. Sh. Liptser, A. N. Shiryaev, “On the question of absolute continuity and singularity of probability measures”, Math. USSR-Sb., 33:2 (1977), 203–221
\Bibitem{KabLipShi77}
\by Yu.~M.~Kabanov, R.~Sh.~Liptser, A.~N.~Shiryaev
\paper On the question of absolute continuity and singularity of probability measures
\jour Math. USSR-Sb.
\yr 1977
\vol 33
\issue 2
\pages 203--221
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