Transcription of Expected Value and Markov Chains - aquatutoring.org
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Expected Value and Markov Chains - aquatutoring.org
Expected Value and Markov ChainsKaren GeSeptember 16, 2016 AbstractAMarkov Chainis a random process that moves from one state toanother such that the next state of the process depends only on wherethe process is at the present state. Anabsorbing stateis a statethat is impossible to leave once reached. We survey common methodsused to find the Expected number of steps needed for a random walkerto reach an absorbing state in a Markov chain . These methods are:solving a system of linear equations, using a transition matrix , andusing a characteristic :probability, Expected Value , absorbing Markov Chains ,transition matrix , state diagram1 Expected ValueIn this section, we give a brief review of some basic definitions, properties,and examples of Expected the random variableXtake on valuesx1,x2,x3.
The matrix N= (I Q) 1 is called the fundamental matrix for P. The entry n ij of Ngives the expected number of times that the process is in the transient state jif it started in the transient state i. (See [1] for a proof.) Since I Q= 0 @ 1 1 0 1=5 3=5 2=5 0 2=5 3=5 1 A; we can use Gauss-Jordan elimination to calculate its inverse matrix and get ...
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