Expectation of 1st passage time for BM

ralfbuesser · July 6th, 2016, 1:31 pm

Hi,Is there a closed-form solution for the expectation of the first passage time for a Brownian motion. If so, can you point me to a good reference?Thanks and regardsRalf

Alan · July 6th, 2016, 5:57 pm

yes -- standard stuff.See Karlin & Taylor ('A Second Course in Stochastic Processes'), pgs 192-193 or Prop. 1.6 in http://www.columbia.edu/~ks20/FE-Notes/ ... tes-BM.pdf Note that, without a drift in the direction of the level being hit, the answer is [$]+\infty[$].

ralfbuesser · July 7th, 2016, 5:59 pm

thanks for that, Ralf.

ralfbuesser · July 7th, 2016, 6:00 pm

thanks for that, Ralf.

Cuchulainn · July 8th, 2016, 9:12 am

More generally, pde approach