Calculate continuous time transition probabilities
tpm_cont.Rd
A continuous-time Markov chain is described by an infinitesimal generator matrix \(Q\). When observing data at time points \(t_1, \dots, t_n\) the transition probabilites between \(t_i\) and \(t_{i+1}\) are caluclated as $$\Gamma(\Delta t_i) = \exp(Q \Delta t_i),$$ where \(\exp()\) is the matrix exponential. The mapping \(\Gamma(\Delta t)\) is also called the Markov semigroup. This function calculates all transition matrices based on a given generator and time differences.
Arguments
- Q
infinitesimal generator matrix of the continuous-time Markov chain of dimension c(N,N)
- timediff
time differences between observations of length n-1 when based on n observations
- ad
optional logical, indicating whether automatic differentiation with
RTMB
should be used. By default, the function determines this itself.- report
logical, indicating whether
Q
should be reported from the fitted model. Defaults toTRUE
, but only works ifad = TRUE
.