DES - Definition of 'Continuous Time Homogeneous Markov Chain (CTHMC)'

Continuous Time Homogeneous Markov Chains:

A continuous-time homogeneous Markov Chain is a stochastic process such that:

• the time set $\mathcal{T}$ is continuous, typically $\mathcal{T}={\mathbb{R}}^{\ge 0}$
• the state set $\mathcal{X}$ is discrete, typically $\mathcal{X}=\{1,2,3,\dots \}$
• the Markov property holds.
• the homogeneity holds.

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~Example: