Variance-covariance matrix of an OU process with optional measurement error and jump at the start

Variance-covariance matrix of an OU process with optional measurement error and jump at the start

PCMCondVOU(
  H,
  Sigma,
  Sigmae = NULL,
  Sigmaj = NULL,
  xi = NULL,
  e_Ht = NULL,
  threshold.Lambda_ij = getOption("PCMBase.Threshold.Lambda_ij", 1e-08)
)

Arguments

H

a numerical k x k matrix - selection strength parameter.
Sigma

a numerical k x k matrix - neutral drift unit-time variance-covariance matrix.
Sigmae

a numerical k x k matrix - environmental variance-covariance matrix.
Sigmaj

is the variance matrix of the normal jump distribution (default is NULL).
xi

a vector of 0's and 1's corresponding to each branch in the tree. A value of 1 indicates that a jump takes place at the beginning of the branch. This arugment is only used if Sigmaj is not NULL. Default is NULL.
e_Ht

a numerical k x k matrix - the result of the matrix exponential expm(-t*H).
threshold.Lambda_ij

a 0-threshold for abs(Lambda_i + Lambda_j), where Lambda_i and Lambda_j are eigenvalues of the parameter matrix H. This threshold-values is used as a condition to take the limit time of the expression `(1-exp(-Lambda_ij*time))/Lambda_ij` as `(Lambda_i+Lambda_j) --> 0`. You can control this value by the global option "PCMBase.Threshold.Lambda_ij". The default value (1e-8) is suitable for branch lengths bigger than 1e-6. For smaller branch lengths, you may want to increase the threshold value using, e.g. `options(PCMBase.Threshold.Lambda_ij=1e-6)`.

Value

a function of one numerical argument (time) and an integer indicating the branch-index that is used to check the corresponding element in xi.