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On the transition density of a multidimensional parameter Wiener process with one barrier

Published online by Cambridge University Press:  14 July 2016

E. M. Cabaña
E. M. Cabaña*
Affiliation:
Universidad Simón Bolívar
*
∗ Postal address: Department of Mathematics, Universidad Simón Bolívar, Apartado Postal No. 80659, Caracas, Venezuela.
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Abstract

An upper estimate of the probability density of d-parameter Wiener process with one barrier, already known for d = 2, is extended for general d.

Keywords

BARRIER PROBLEMMULTIVARIATE KOLMOGOROV–SMIRNOV TEST
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 1 , March 1984 , pp. 197 - 200
Copyright
Copyright © Applied Probability Trust 1984 

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References

[1] Cabaña, E. M (1975) Una aplicación estadística del movimiento browniano plano. CIENES.Google Scholar
[2] Cabaña, E. M. and Wschebor, M. (1982) The two-parameter Brownian bridge: Kolmogorov inequalities and upper and lower bounds for the distribution of the maximum. Ann. Prob. 10, 289–302.CrossRefGoogle Scholar
[3] Goodman, V. (1976) Distribution estimates for functionals of the two-parameter Wiener process. Ann. Prob. 4, 977–982.CrossRefGoogle Scholar
[4] Pyke, R. (1975) Multidimensional empirical processes: some comments. In Statistical Inference and Related Topics, ed. Puri, M. L., Academic Press, New York, 45–48.CrossRefGoogle Scholar