ctmcbd
Returns the infinitesimal generator matrix for a
continuous birth-death process over the finite state space
. For each ,
b(i) is the transition rate from state to
state , and d(i) is the transition rate from state
to state .
Matrix is therefore defined as:
$$ \pmatrix{ -\lambda_1 & \lambda_1 & & & & \cr \mu_1 & -(\mu_1 + \lambda_2) & \lambda_2 & & \cr & \mu_2 & -(\mu_2 + \lambda_3) & \lambda_3 & & \cr \cr & & \ddots & \ddots & \ddots & & \cr \cr & & & \mu_{N-2} & -(\mu_{N-2}+\lambda_{N-1}) & \lambda_{N-1} \cr & & & & \mu_{N-1} & -\mu_{N-1} } $$
where and are the birth and death rates, respectively.
See also: dtmcbd