Alright, so I am trying to simulate a value and its not working out the way I expect. I think I narrowed down my an issue to me simulating the integral of brownian bridge process. I know that 1000 iid random variables were used to approximate the Brownian motions in my simulation.
Let be a standard brownian bridge process. I want to simulate the following (its something more complicated but I think the issue is here):
This was my technique (in R)
library(e1071) # for the rbridge function
x1 = rbridge(end = 1, frequency = 1000)
x2 = rbridge(end = 1, frequency = 1000)
Q = sum(t(x1)%*%x2)
Help appreciated. And I doing this part correctly?