= Holding probability of a Markov chain
{title2=$P(x,x)$}
= Holding probabilities of a Markov chain
{synonym}
At state $x$, the holding probability of a discrete-time <Markov chain> is the self-transition probability $P(x,x)$. It is the conditional probability that the next state remains $x$. In a nearest-neighbour <birth-death chain>, it is $1-p_x-q_x$, where $p_x$ and $q_x$ are the probabilities of stepping right and left. Holding changes the elapsed time but not the embedded chain of actual moves or its boundary exit probabilities.
Back to article page
