Continuous time Markov chain
Ming Liao · 2013
Denition: A continuous time and discrete state processX(t) is called a continuous time Markov chain if it has the following Markov property in continuous time: For any 0 s1 0, and states i1; i2; : : : ; in; i; j, P [X(s+ t) = j j X(s1) = i1; X(s2) = i2; : : : ; X(sn) = in; X(s) = i] = P [X(s+ t) = j j X(s) = i]: (5.1) This means that given the present (time s), the distribution of the future (time s+ t) is independent of the past (time < s).