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Stochastic Process (SP): A SP in discrete time t ε N = {0, 1, 2, …} is a
sequence of time-indexed RVs X0, X1, X2, …, with X = {Xt, t ≥ 0}.
Discrete-Time Markov Chain (DTMC): A SP, X = {Xt, t ≥ 0}, is a DTMC if,
for all t, Pr(Xt+1 = j | Xt = a, Xt-1 = b, Xt-2 = c, …) = Pr(Xt+1 = j | Xt = a).
Pr(Xt+1 = j | Xt = a, Xt-1 = b, Xt-2 = c, …) = Pr(Xt+1 = j | Xt = a) = Pij
lec9.pptx
lec9.pptx
lec9.pptx
lec9.pptx
lec9.pptx
lec9.pptx
lec9.pptx
lec9.pptx
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lec9.pptx

  • 1. Stochastic Process (SP): A SP in discrete time t ε N = {0, 1, 2, …} is a sequence of time-indexed RVs X0, X1, X2, …, with X = {Xt, t ≥ 0}. Discrete-Time Markov Chain (DTMC): A SP, X = {Xt, t ≥ 0}, is a DTMC if, for all t, Pr(Xt+1 = j | Xt = a, Xt-1 = b, Xt-2 = c, …) = Pr(Xt+1 = j | Xt = a). Pr(Xt+1 = j | Xt = a, Xt-1 = b, Xt-2 = c, …) = Pr(Xt+1 = j | Xt = a) = Pij