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Distribution of Brownian Bridge
I know from Karatzas & Shreve (1991) that a Brownian Bridge B(t) from a to b on time interval [0,T] satisfies: B(t)=a(1-t/T) + b*t/T + [W(t) - W(T)*t/T], where W(t) is a standard one-dimensional Brownian motion.By the above equation we can get its distribution. My question is what's the distribution of the Brownian Bridge B(t) from a to b on time interval [T1, T2], where T1 is NOT 0?Any idea or reference?
Distribution of Brownian Bridge
It seems just relabelling to me: t -> t- T1 and T -> T2-T1