α-Wiener Bridges: Singularity of Induced Measures and Sample Path Properties

Let us consider the process [image omitted] given by the SDE [image omitted], t[0, T), where , T(0, ), and (Bt)t epsilon 0 is a standard Wiener process. In case of 0, the process X() is known as an -Wiener bridge, in case of =1 as the usual Wiener bridge. We prove that for all , , , the probability measures induced by the processes X() and X() are singular on (C[0, T), B(C[0, T))). Further, we investigate regularity properties of [image omitted] as tT.