Friday, April 15, 2016

stochastic processes - Brownian motion - first passage time



Can anyone point me to the expression for the first passage time for a geometric Brownian motion process X(t) as a function of the starting point, threshold, drift and diffusion parameters.


I am mainly interested for processes with positive drift and thresholds that are higher than the starting point.


I know this is a standard expression, however all results I have found so far are specific to a particular starting point (e.g. X(0) = 0) and/or threshold of 1, and I am not sure how to generalize to any initial state and threshold value.


Any help would be much appreciated


Thanks




No comments:

Post a Comment

technique - How credible is wikipedia?

I understand that this question relates more to wikipedia than it does writing but... If I was going to use wikipedia for a source for a res...