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

Paul Deheuvels

Stochastic Processes and their Applications, 1982, vol. 13, issue 3, 311-318

Abstract: 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.

Keywords: Brownian; bridge; Wiener; process; non-parametric; statistics (search for similar items in EconPapers)
Date: 1982
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