- Joined
- 6/11/10
- Messages
- 189
- Points
- 28
The reflection principle is a fine tool to solve barrier ending density as
The distribution for a simple Brownian Motion ending value WT given a single barrier b was hit during (0,T] is
N(x-b,sqrt(T))
I doubt if there are two other ways to solve this problem:
reach (b,b+db) at some time t, and then arrive at (x,x+dx) at time T, integrate the two integrals with respect to t
hit b within some time interval (t,t+dt), and then arrive at (x,x+dx) at time T
Can anyone solve the convolution integral and prove the results are the same?
(y)
The distribution for a simple Brownian Motion ending value WT given a single barrier b was hit during (0,T] is
N(x-b,sqrt(T))
I doubt if there are two other ways to solve this problem:
reach (b,b+db) at some time t, and then arrive at (x,x+dx) at time T, integrate the two integrals with respect to t
hit b within some time interval (t,t+dt), and then arrive at (x,x+dx) at time T
Can anyone solve the convolution integral and prove the results are the same?
(y)