2016/12/27 by Xue-Mei Li, Li, Xue-Mei
Economics, Econometrics and Finance · Mathematics · #58J65 #60 H07 #60Bxx #60Dxx #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1612.08716
openalex publication_date 2016/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.