Return time from a three-state chain

MediumStochastic Processes~5m

A Markov chain on $\{A,B,C\}$ moves as follows: from $A$ it goes to $B$ or $C$ with probability $1/2$ each; from $B$ it goes to $A$ with probability $1$ ; from $C$ it goes to $A$ with probability $3/4$ and stays at $C$ with probability $1/4$ . Starting at $A$ , what is the expected number of steps to first return to $A$ ? (to 3 decimals)

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First solve $\pi = \pi P$ for the stationary probability of $A$ (don't forget the self-loop at $C$ ).
Then the return time is $1/\pi_A$ .

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2.1667 (± 0.005)

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Interview format: Prop Trading, Systematic & Data-Driven Trading

Return time from a three-state chain

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