This pacakge provides functions to solve continuous time Markov chains for state probablities or accumulated sojourn times at a certain time point, including time infinity.
Here's a detailed tutorial on how to use this package.
The following example is about solving a 4 states birth-death chain at time 0.1, 1.0, and infinity.
using MarkovChains
chain = ContMarkovChain()
n0 = add_state!(chain)
n1 = add_state!(chain)
n2 = add_state!(chain)
n3 = add_state!(chain)
add_transition!(chain, n0, n1, 1.0) #transition from n0 to n1 with rate = 1.0
add_transition!(chain, n1, n2, 1.0)
add_transition!(chain, n2, n3, 1.0)
add_transition!(chain, n3, n2, 3.0)
add_transition!(chain, n2, n1, 2.0)
add_transition!(chain, n1, n0, 1.0)
init_prob = sparsevec([1], [1.0])
sol = solve(chain, init_prob, 0.1) #solve at time 0.1
@show state_prob(sol, n1) #probablity of being at state n1 at time 0.1
# state_prob(sol, n1) = 0.08652421409974947
sol = solve(chain, init_prob, 1)
@show state_prob(sol, n1)
# state_prob(sol, n1) = 0.375
sol = solve(chain, init_prob, Inf)
@show state_prob(sol, n1)
# state_prob(sol, n1) = 0.375The following example is about solving a 3 states chain with absorbing states.
chain = ContMarkovChain()
n1 = add_state!(chain)
n2 = add_state!(chain)
n3 = add_state!(chain)
add_transition!(chain, n1, n2, 2.0)
add_transition!(chain, n2, n3, 4.0)
init_prob = sparsevec([1], [1.0])
sol = solve(chain, init_prob, 0.5)
@show state_prob(sol, n2)
# state_prob(sol, n2) = 0.23254415793482963
@show state_cumtime(sol, n2) #cumulative time spent in state n2
# state_cumtime(sol, n2) = 0.09989410022321275
@show mean_time_to_absorption(chain, init_prob) #you may be interested in MTTA for a chain with absorbing states
# mean_time_to_absorption(chain, init_prob) = 0.75