I have this BM(Wiener process) which i need to simulate:
Where sigma1 = 1
I know that the standard deviation of B1(t) is sqrt(t), so if we wouldnt have the constant sigma1, the simulation we would have would be: Normal(0: mean, variance: sqrt(t))
But im not sure in general what happens when you have a constant like sigma outside B1? By that I am wondering, is the simulation going to be: Normal(0: mean, variance: sqrt(t * sigma1) ? or: Normal(0: mean, variance: (sqrt(t) * sqrt(B1)) ? or Normal(0: mean, variance: sqrt(t) * sigma1) ? or something else ?