On a Certain Metric on the Space of Pairs of a Random Variable and a Probability Measure

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J. Math. Sci. Univ. Tokyo
Vol. 8 (2001), No. 2, Page 343--356.

Kusuoka, Shigeo ; Nakayama, Toshiyuki
On a Certain Metric on the Space of Pairs of a Random Variable and a Probability Measure
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Abstract:
The authors introduce new metrics on the space of pairs of a random variable and a probability measure over a Polish space, and study the properties of them. Finally, as an application, they discuss how the integrand for the martingale representation converges in the invariance principle.

Mathematics Subject Classification (1991): Preliminary 60B10; Secondary 60B5

Mathematical Reviews Number: MR1837168

Received: 2000-10-02

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