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For a discrete Markov chain random walk with p < 0.5 with state space S= {0,1,2..} What is the stationary distribution?

I could use any help.

Thank you

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1 Answer 1

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If $a_n$ is the probability of being in position $n$, use first-step analysis to get $$ a_n=p a_{n-1} + (1-p)a_{n+1},\quad n\ge 1,\quad\text{and} $$ $$ a_0=(1-p)a_0+(1-p)a_1. $$ This can then be readily solved for the $a_n$.

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