Sorry for cross-posting, I'm really eager on getting an answer!Here is the question:S follows a Brownian motion with zero drift and constant volatility, i.e. its std dev is sigma*(t^1/2) at time t and sigma is a known constant.we know that at time T, the process has value B. Now we start at time 0. wat is the probability of the process having value never higher than A during time 0 to T?i.e. what is the probability that the maximum value of the process in time 0 to T is less than A? Assume constants A > B.Or more generally, ignore B, what is the probability the process always stays below A during time 0 to T?Thanks a million!!

first entry inhttp://www.google.com/search?as_q=&num=10&hl=e ... afe=images

It's a classical problem whose solution is mainly based on reflection principle. It would be tedious to write the solution here but you will find good references on the web. For instance course has a section (number 7) devoted to that subject. And don't worry it's written in english!

Thanks for the replies!Does anyone knows how to derive the result using Bayesian probability method?

I'm not sure what you mean by 'deriving it using a Bayesian probability method' - Bayesian method are less applicable for problems that have definite mathematical answers.However, one possible means of deriving it using a Bayesian probability method would be to start off with a prior distribution for the probability. Then, do lots of Brownian motion simulations, and you can update your prior to get a posterior distribution.