Abstract:
We prove a rather general comparison principle for the distribution functions of random variables. As a consequence, we obtain a criterion for the equivalence, in distribution in the vector sense, of an arbitrary sequence of random variables to the Rademacher system; we study the applications of this principle to special cases.
Keywords:
distribution function of a random variable, comparison principle, Rademacher system, Banach space, Chebyshev inequality, Peetre K-functional, Banach couple.
Citation:
S. V. Astashkin, “On the Comparison of Distribution Functions of Random Variables”, Mat. Zametki, 87:1 (2010), 17–25; Math. Notes, 87:1 (2010), 15–22