absorb: Absorbing Markov Chain
In SonmezOzan/mc_1.0.3: Markov Chains

Description Usage Arguments Details Value Author(s) Examples

Finds key features of a Discrete Finite absorbing Markov Chain. Future updates will include the infinite case

1	absorb.mc(pijdef, type, tol = 1e-06, ...)

`pijdef`	The transition probabilities, either in matrix form or a function For now only matrix form, until the infinite case is incorporated
`type`	Type of markov chain, either 'discrete' or 'continuous'.
`tol`	A positive scalar for error tolerance for infinite markov chain approximation.
`...`	Additional argument for continuous markov chain type.

This function generates key features and common output for an absorbing Markov Chain. An error is returned if the input matrix is not absorbing. A Markov Chain is an absorbing chain if 1) At least one state is absorbing 2) All non-absorbing states are transient.

Object of class "mc", with components

`pijdef`	The original transition matrix
`absorb`	TRUE,Confirms it is an absorbing chain
`astates`	absorbing states
`tstates`	transient states
`canonicalForm`	canonical form of the transition matrix
`steady.state`	stationary distribution
`FundamentalMatrix`	fundamental matrix
`Qmat`	Q matrix, the sub matrix of transient to transient states
`Rmat`	R matrix, the sub matrix of transient to absorbing states
`ExpectedHits`	Expected number of hits in state i before getting absorbed
`AbsorbProb`	A matrix of absorption probalities. Columns represent the absorbing states, rows represent transient states. The i,j entry represents the probablilty of being absorbed into absorbing state j given you are in state i

Teresa Filshtein <teresa.filshtein@gmail.com>,Ozan Sonmez <osonmez@ucdavis.edu>, Rex Cheung <rccheung@ucdavis.edu>, and Norm Matloff <matloff@cs.ucdavis.edu>

#Discrete Chain
#Finite state


drunkard = t(matrix(c(1,rep(0,4),.5,0,.5,0,0,0,.5,0,.5,0,0,0,.5,0,.5,
                    rep(0,4),1),nrow = 5))
absorb.mc(drunkard)$ExpectedHits
absorb.mc(drunkard)$AbsorbProb