## Simulation of a Gaussian process

### Description

Simulate the trajectory of a Gaussian process, given a mean vector and a variance-covariance structure.

### Usage

sim_gaussianProcess(
mean_vec,
varCov_mat,
from = 0,
to = 1,
start = 0,
nb.points = 10
)


### Arguments

 mean_vec Vector (if multimensional) of means for the increments following gaussian distribution. varCov_mat Corresponding variance-covariance structure. from Initial time point at which the process is simulated. to Last time point at which the process is simulated. start Useful if the user wants to make the trajectory start from some given value. nb.points Number of points at which the process is simulated.

### Value

The trajectory of the Gaussian processes after simulating the multivariate Gaussian distributions with specified variance-covariance structure.

### Author(s)

Xavier Milhaud xavier.milhaud.research@gmail.com

### Examples

list.comp <- list(f1 = "norm", g1 = "norm")
list.param <- list(f1 = list(mean = 12, sd = 0.4),
g1 = list(mean = 16, sd = 0.7))
sample1 <- rsimmix(n = 2000, unknownComp_weight = 0.5, comp.dist = list.comp,
comp.param = list.param)$mixt.data ## First get the variance-covariance matrix of the empirical process (Donsker correlation): cov_mat <- .Call('_admix_estimVarCov_empProcess_Rcpp', PACKAGE = 'admix', seq(from = min(sample1), to = max(sample1), length.out = 100), sample1) ## Plug it into the simulation of the gaussian process: B1 <- sim_gaussianProcess(mean_vec=rep(0,nrow(cov_mat)), varCov_mat=cov_mat, from=min(sample1), to = max(sample1), start = 0, nb.points = nrow(cov_mat)) plot(x = B1$dates, y = B1\$traj1, type="l", xlim = c(min(sample1),max(sample1)), ylim = c(-1,1))