Markov processes. How to calculate the probability that the system will be in state 1 at step 7, if it started in state 2 and from the third step?

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Soobit2016-03-10 23:30:17

Mathematics

Soobit, 2016-03-10 23:30:17

Markov processes. How to calculate the probability that the system will be in state 1 at step 7, if it started in state 2 and from the third step?

The system starts from step 3 in state 2 and with some probabilities changes states (1-4) up to step 7. Ends in state 1. When calculating the probability, how to take into account the fact that the system started from step 3?
P - transition matrix, Q - transition vector to state 1.
(P^4) * Q - probability of being in state 1 by 5 "day" (according to Kolmogorov's equation)
What to do next?

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