Hi markov chain specialist,
Hope you can give me an answer regarding this trellis diagram that i saw on a book. why in this picture of a general first-order markov chain of 2 states,we should know the prob. of each state at each time?
A general first-order markov chain, can be Time-dependent(non stationary) so Transition prob. can change by time. That's why we have E(time) in this picture at each time. but by having the initial Prob. of each state (P(t=1)), and Transition prob. i can calculate prob. of each state in any given time, so The state probabilities at each time (P(t=2,t=3,...)) are Extra informations. am i right or i ignore something?
pic.Statistics in Volcanology (google books) page 167 MArkov chain