What kind of chain is an absorbing Markov chain?
An absorbing Markov chain A common type of Markov chain with transient states is an absorbing one. An absorbing Markov chain is a Markov chain in which it is impossible to leave some states, and any state could (after some number of steps, with positive probability) reach such a state.
Can a Markov chain have an infinite state space?
An absorbing state is a state that, once entered, cannot be left. Like general Markov chains, there can be continuous-time absorbing Markov chains with an infinite state space. However, this article concentrates on the discrete-time discrete-state-space case.
When does the coin flip cease in the absorbing Markov chain?
Although in reality, the coin flips cease after the string “HTH” is generated, the perspective of the absorbing Markov chain is that the process has transitioned into the absorbing state representing the string “HTH” and, therefore, cannot leave. The expected number of steps starting from each of the transient states is
What are the typical rates of transition between Markov states?
The typical rates of transition between the Markov states are the probability p per unit time of being infected with the virus, w for the rate of window period removal (time until virus is detectable), q for quit/loss rate from the system, and d for detection, assuming a typical rate
Which is the minimum number of steps to an absorbing state?
In the same example, the minimum number of steps to go from state 3 to an absorbing state (state 5) is 2 with probability 0.25. For each non-absorbing state , let be the probability that, starting from state , the process will take more than steps to reach an absorbing state.
Which is the absorbing state of the matrix?
The above matrix can be interpreted as a small scaled random walk or a small scaled gambler’s ruin. It has two absorbing states, 0 and 5. Once the process reaches these states, it does not leave these states. The other states (1, 2, 3 and 4) can reach an absorbing state in a finite number of steps with a positive probability.
What is the probability of being absorbed into a state?
More specifically, the row in corresponding to transient state multiplying the column in corresponding to the absorbing state results in the probability of being absorbed into state given that the process start in state .