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A stochastic process describes the evolution of random variables/systems over time and/or space and/or any other index set. It has applications in areas such as econometrics, weather, signal processing, etc. Examples: Gaussian process, Markov process, etc.
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Expected Number of Transitions for a Markov Chain to Reach a Certain State
You can also do an exact calculation. Let $K(x,y)$ be the transition probability for going from point $x$ to point $y$ in some Markov chain. For points $a,b$, let $\tau_{a,b}$ be the expected time to …