Markov

MARKOV ANALYSIS

Markov analysis is a technique that deals with the probabilities of future occurrences by analyzing presently known probabilities. Markovian processes are usefull for studying the evolution of systems during several periods where the state of each period cannot be determined with certainty. To do this we utilize transition probabilities. We are therefore interested in knowing the probability that a system will be in a particular state during a certain period of time. This technique has numerous applications in business, including market share analysis, bad debt prediction, enrollment predictions and machine breakdown.

During this course we will concentrate on Markov chains with stationary transition probabilities. For this we will include the following assumptions:

There are a limited or finite number of possible states

The probability of changing states remains the same over time

STATES. ID all possible conditions of a process or system. States are collectively exhaustive and mutually exclusive. The probabilities of these states, therefore, add to one.

Suppose there are only four supermarket stores in a section of the city, WalMart, CM, Chedraui and Soriana. Therefore there are four states represented by each grocery store. A supermarket customer can only be in one of these four stores or states. The market shares of each represents the probability of the current state occurring.

Vector of State Probabilities, depicts the probability that the system is in a certain state.

Π(i) = vector of state probabilities for period (i) = (Π1, Π2, Π3,…, Πn)

n = number of states

Π1= probability of being in state 1

Π2= probability of being in state 2

Πn= probability of being in state n

We can predict any future state from the previous one and the matrix of transition probabilities.

The system remains stable (no new players or dropouts).

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