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Markov Chains

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1Markov ChainslPROPERTIESlREGULAR Markov CHAINSlABSORBING Markov CHAINSProperties of Markov Chains Introduction Transition & State Matrices Powers of Matrices Applications2Andrei Markov1856 -- 1922Examples of Stochastic Processes1)Stock Market UP DOWN UNCHANGED2)Brand Loyalty:Stay with brand ASwitch to brand ASwitch away from brand A3)Brownian MotionProduct LoyaltyA marketing campaign has the effect that:80 % of consumers who use brand A stay with it (so 20% switch away from it)60 % consumers who use other brands switch to brand AWhat happens in the long run?Problem: FEEDBACK!

Markov Chains or Processes • Sequence of trial with a constant transition matrix P • No memory (P does not change, we do not know whether or how many times P has already been applied) 6 A Markov process has n states if there are n possible outcomes. In this case each state matrix has n entries, that is each state matrix is a 1 x n matrix.

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