I am trying to find E[B(t1)*B(t2)*B(t3)] with essentially no information other than B(0)=0 and t1<t2<t3. I am very unsure of what this means. I have limited knowledge of Brownian motion since, for the most part, I have not understood what I have learned in class. I'm not looking for a direct answer, but I need some help figuring out how to go about this problem.
From my notes, I know that when B(0)=0, B(t) is approximately normal with mean 0 and standard deviation t.
I'm not even sure what the expected value of a product of B(t)'s means. Can someone explain this to me in words?
Apr 24th 2011, 02:13 AM
Hi! I don't know if this what I think is right. Brownian motion has two very important properties, it has stationary increments and independents incremenets. And it means that increments does depend only on length of interval. So in my opinion
E(B(t1)*B(t2)*B(t3)) = E(B(t1)*(B(t2-t1)+B(t1))*(B(t3-t2)+B(t2-t1)+B(t1))
as I said, Im not sure of it, but in my opinion it looks ok.
do you know how to solve it?