Function Reference: dtmcbd

Function File: P = dtmcbd (b, d)

Returns the transition probability matrix P for a discrete birth-death process over state space 1, …, N. For each i=1, …, (N-1), b(i) is the transition probability from state i to (i+1), and d(i) is the transition probability from state (i+1) to i.

Matrix \bf P is defined as:

$$ \pmatrix{ (1-\lambda_1) & \lambda_1 & & & & \cr \mu_1 & (1 - \mu_1 - \lambda_2) & \lambda_2 & & \cr & \mu_2 & (1 - \mu_2 - \lambda_3) & \lambda_3 & & \cr \cr & & \ddots & \ddots & \ddots & & \cr \cr & & & \mu_{N-2} & (1 - \mu_{N-2}-\lambda_{N-1}) & \lambda_{N-1} \cr & & & & \mu_{N-1} & (1-\mu_{N-1}) } $$

where \lambda_i and \mu_i are the birth and death probabilities, respectively.

See also: ctmcbd

Example: 1

  

 birth = [ .2 .3 .4 ];
 death = [ .1 .2 .3 ];
 P = dtmcbd( birth, death );
 disp(P)

   0.8000   0.2000        0        0
   0.1000   0.6000   0.3000        0
        0   0.2000   0.4000   0.4000
        0        0   0.3000   0.7000