Transition matrix of the embedded jump chain

Computes, from the generator \(Q\) of a continuous time Markov chain, the transition matrix of its embedded (jump) chain: the probability of jumping from \(i\) to \(j \ne i\) is \(-Q_{ij} / Q_{ii}\).

Usage

generatorToTransitionMatrix(gen, byrow = TRUE)

Arguments

gen

A generator matrix: non-negative off-diagonal rates, with rows (or columns, if byrow = FALSE) summing to zero.

byrow

Logical: are the rates out of each state in its row (default) or in its column? The result has the same orientation.

Value

The transition matrix of the embedded chain, with the dimnames of gen. A state with zero exit rate (absorbing) gets probability 1 of staying where it is.

References

Anderson, D. F. (2013). Introduction to Stochastic Processes with Applications in the Biosciences. University of Wisconsin at Madison.

See also

Other continuous time Markov chains: ExpectedTime(), ctmcFit(), freq2Generator(), impreciseProbabilityatT(), is.CTMCirreducible(), is.TimeReversible(), probabilityatT(), rctmc(), transition2Generator()

Author

Sai Bhargav Yalamanchi

Examples

energyStates <- c("sigma", "sigma_star")
gen <- matrix(c(-3, 3, 1, -1), nrow = 2, byrow = TRUE,
              dimnames = list(energyStates, energyStates))
generatorToTransitionMatrix(gen)
#>            sigma sigma_star
#> sigma          0          1
#> sigma_star     1          0