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A convergence property of Dubins' representation of distributions

Published online by Cambridge University Press:  17 April 2009

Shey Shiung Sheu
Shey Shiung Sheu
Affiliation:
Institute of Applied Mathematics, National Tsing Hua University, Hsinchu, Taiwan, 300043, Republic of China
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Abstract

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Let (Xn)n≥1 be a sequence of random variables with zero means and uniformly bounded variences. Let τn be the stopping time defined on a given Brownian motion (Bt)t≥0, B0 = 0, by Dubins' method such that B(τn) has the same distribution as Xn. We prove that Xn converging to 0 in distribution implies that τn converges to 0 in probability. Examples are presented to illustrate the result is the best possible.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 1 , August 1988 , pp. 83 - 85
Copyright
Copyright © Australian Mathematical Society 1988

References

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