The discussion revolves around the distribution of the sum of two standard Brownian motions, specifically examining the properties of B(u) + B(v) where u and v are non-negative. Participants are exploring the mean and variance of this sum.
The discussion is active with participants questioning assumptions about independence and variance calculations. Some guidance has been offered regarding the properties of Brownian motion, but no consensus has been reached on the correctness of the variance expression.
Participants are addressing specific properties of Brownian motion, including independence and variance, while also considering the implications of their calculations. There is a focus on ensuring the assumptions made are valid within the context of the problem.
BrownianMan said:B(t) is a standard Brownian Motion. u and v are both => 0. What is the distribution of B(u) + B(v)?
The mean is 0.
For the variance I get Var(B(u)+B(v)) = u+v. Is this right?
BrownianMan said:Aren't B(u) and B(v) independent? If so, then the variance of their sum should be the sum of their variance.