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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 13, Fasc. 1,
pages 39 - 58
 

WEAK CONVERGENCE UNDER MAPPING

Władysław Szczotka

Abstract: For a given random element X of a metric space S and a measurable mapping h of S into a metric space S 1 such that P (X (- D ) > 0 h we give the conditions for a sequence of random elements X , n n > 1, of the space S under which the convergence D Xn - --> X implies D h(Xn) ---> h(X) (Lemma 1) and stronger conditions for (Xn) under which the convergence Xn -D--> X implies D (Xn,h(Xn)) ---> (X, h(X)) (Theorem 3). Here Dh is the set of discontinuities of h . The case S = D[0, oo ), h(x) = sup0<t< oo x(t) is considered in detail.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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