P{X(t+s) = j | X(s) = i, X(u) = x(u), for 0 <= u < s} = P{X(t+s) = j | X(s) = i}The conditional distribution of the future X(t+s) given the present and the past X(u), 0 <= u < s, depends only on the present and is independent of the past.
Drew an unexpected life lesson during a statistics lecture on Continuous Time Markov Chain... and immediately wondered if I had been getting sufficient rest. In other news, spoke with an amazing friend about how the past two weeks have been and it's a great burden off my heart (: Praise God!
A large portion of today's linguistics tutorial comprised an in-depth discussion about the presuppositions surrounding "Where did you put the cheese?" Apart from being highly amused at the absurdity of it all, it also made me think of cheese on toast and grilled brie <3 right before lunch. (& ya'll know my take on school food...)
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