-Wiener bridges: singularity of induced measures and sample path properties. (English) Zbl 1195.60060
Summary: Let us consider the process given by the SDE , , where , , and is a standard Wiener process. In case of , the process is known as an -Wiener bridge, in case of as the usual Wiener bridge. We prove that for all , , the probability measures induced by the processes and are singular on . Further, we investigate regularity properties of as .
|60G30||Continuity and singularity of induced measures (stochastic processes)|
|60G17||Sample path properties|