Sample Question #167 (applied math)

Can you write down the formal definition of a Markov chain (or Markov process)? What’s the transition probability function of a Markov process?

(Comment: the second part of the question is a good example of how some interviewers will probe you on minor details of a topic)

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ANSWER

Don’t forget that a Markov chain can be either continuous or discrete. I’ll give the definition for the continuous case.

A time series X(t) is a Markov chain (or Markov process) if its conditional distribution function satisfies Pr{X(u) | X(s), s<=t} = Pr{X(u) | X(t)}, where u > t. (Bonus question: what does this definition mean in plain English?)

The transition probability function is Pr{X(u) belongs_to A | X(t) = θ}, u > t, where A is a subset of the value space of X(t).