Generalised Brownian bridges: examples

Xue-Mei Li

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arXiv · 1612.08716

Generalised Brownian bridges: examples

Xue-Mei Li

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Abstract

We observe that the probability distribution of the Brownian motion with drift $-c \frac x {1-t}$ where $c\not =1$ is singular with respect to that of the classical Brownian bridge measure on $[0,1]$, while their Cameron-Martin spaces are equal set-wise if and only if $c> \frac 12$, providing also examples of exponential martingales on $[0,1)$ not extendable to a continuous martingale on $[0,1]$. Other examples of generalised Brownian bridges are also studied.

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Xue-Mei Li. 2016-12-27. Generalised Brownian bridges: examples. https://arxiv.org/abs/1612.08716

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