Is hitting time of Brownian motion independent

Suppose that $B_t$ is a standard Brownian Motion. And $T_a$ $T_b$ are the hitting time whereas $a<0$, $b>0$. Then are these two rand开发者_运维百科om variables independent?

They are not independent: consider Tb conditional on Ta=T. This equivalent to the hitting time for a+b, which Is clearly different from Tb. You need to give more detail about the question if you want a more rigorous answer.