In my module on Markov processes, the following notation is used: $$ p_{ij}^{(m,n)} = P(X_n = j \mid X_m = i) \quad \text{where } \: m<n \\ p_j^{(n)} = P(X_n = j) \\ p_{ij}^{(k)} = \: ??? $$
Does anyone know what $p_{ij}^{(k)}$ denotes?
2026-04-03 01:16:25.1775178985
What does this notation, used in Markov Chains, mean?
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$$ p_{ij}^{(k)} = \Pr(X_{n+k} = j \mid X_n = i) $$ This is the probability that the process will be in state $j$ at $k$ units of time from now, given that it is in state $i$ now, the $k$-step transition probability.