Since November I've been drinking black coffee two to four times a week. I've always felt unhealthy after drinking coffee; similar to the feeling I get after a meal at McDonald's. But today was the first time I've ever felt that I would vomit if I drank another sip of my coffee. Maybe because I had an semi-empty stomach? I think it is time for me to go back to fun (but expensive and less caffeinated) drinks like Frappuccinos.
Wednesday, January 6, 2010
Friday, January 1, 2010
Feynman-Kac No.1
Here is a problem that I found from an old homework assignment. I've modified the original to make it shorter. Let Wt be Brownian motion and let 1z(x) = 1 if x > z and equals 0 otherwise. Consider the function
where ε is a small number. Write down the PDE satisfied by uε(x,t ; a, T). Show that as ε tends to zero, uε(x,t; a, T) approaches the solution of boundary value problem. Find an analytical expression for uε(x,t; a, T). Use Monte Carlo simulation to evaluate uε(0, 0 ; 1/2, 1) where ε = 0.1, 0.001, and 0.0001.
I'll post my attempt at the solution later. Feel free to add a solution.
where ε is a small number. Write down the PDE satisfied by uε(x,t ; a, T). Show that as ε tends to zero, uε(x,t; a, T) approaches the solution of boundary value problem. Find an analytical expression for uε(x,t; a, T). Use Monte Carlo simulation to evaluate uε(0, 0 ; 1/2, 1) where ε = 0.1, 0.001, and 0.0001.
I'll post my attempt at the solution later. Feel free to add a solution.
Subscribe to:
Comments (Atom)