Continuous-Time Markov Chain (CTMC)
Reference work entry
First Online:
DOI: https://doi.org/10.1007/978-1-4419-1153-7_200073
A Markov process with a continuous parameter but countable state space. The stochastic process {
X(
t)} has the property that, for all
s,
t ≥ 0 and nonnegative integers
i,
j, and
x(
u), 0 ≤
u < ∞,
$$ \begin{array}{ll} \Pr \left\{ {X\left( {t + s} \right) = j|X(s) = i,\,\,X(u) = x(u),\,0 \leq u < s} \right\} \\ \qquad \qquad \quad \quad = \Pr \left\{ {X\left( {t + s} \right) = j|X(s) = i} \right\}. \end{array} $$
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© Springer Science+Business Media New York 2013