Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ib / Paper 1 / 20H / a / Solution

For a stationary <Markov chain> with transition matrix $P$ and stationary distribution $\pi$, the reversed transition matrix is
$$
P^*(x,y)=\frac{\pi(y)P(y,x)}{\pi(x)}.
$$
It is stochastic and has the same stationary distribution.

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 Incoming links: Time-reversed Markov chain