Calculate empirical covariance of the Brownian Motion.
Usage
BMcov(N, M, T, C)
Arguments
N
size of process.
M
number of trajectories.
T
final time.
C
constant positive (if C = 1 it is standard brownian motion).
Value
contour of the empirical covariance for brownian motion.
Details
The brownian motion is a process with increase independent of function the covariance cov(BM) = C * min(t,s), If t > s than cov(BM) = C * s else cov(BM) = C * t.
See Also
BMN simulation brownian motion by the Normal Distribution , BMRW simulation brownian motion by a Random Walk, BMinf brownian motion property(Time tends towards the infinite), BMIrt brownian motion property(invariance by reversal of time), BMscal brownian motion property (invariance by scaling).