Brownian Bridge Marginal Law

Easy

Exercise 1 / 12

Answer

Let $(W_t)$ be a standard Brownian motion and let $0 \le u \le v$ . For $t \in [u,v]$ , define the process

B_t^{u,v} = (W_t - W_u) - \frac{t-u}{v-u}(W_v - W_u).

Question: What is the law of $B_t^{u,v}$ ?

u

)

−

v−ut−u(Wv−

Wu).