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We study sample path deviations of the Wiener process from three differentrepresentations of its bridge: anticipative version, integral representationand space-time transform. Although these representations of the Wiener bridgeare equal in law, their sample path behavior is quite different. Our resultsnicely demonstrate this fact. We calculate and compare the expected absolute,quadratic and conditional quadratic path deviations of the differentrepresentations of the Wiener bridge from the original Wiener process. It isfurther shown that the presented qualitative behavior of sample path deviationsis not restricted only to the Wiener process and its bridges. Sample pathdeviations of the Ornstein-Uhlenbeck process from its bridge versions are alsoconsidered and we give some quantitative answers also in this case.

Sample path deviations of the Wiener and the Ornstein-Uhlenbeck process from its bridges