Invariance of Wiener processes and of Brownian bridges by integral transforms and applications

We find all possible integral equations among a given family which conserve in distribution the Brownian bridge and the Wiener process. The result implies that the Parzen statistic for goodness of fit can be used if and only if the distribution is exponential, direct or reverse, or uniform.

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Year of publication:	1982
Authors:	Deheuvels, Paul
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 13.1982, 3, p. 311-318
Publisher:	Elsevier
Keywords:	Brownian bridge Wiener process non-parametric statistics

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008874927