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Sim.DiffProc (version 2.5)

BMcov: Empirical Covariance for Brownian Motion

Description

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).

Examples

Run this code
## empirical covariance of 200 trajectories brownian standard
BMcov(N=100,M=250,T=1,C=1)

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