## Characterization of the marginal distributions of Markov processes used in dynamic reliability.(English)Zbl 1101.60068

Consider a two-component Markov process $$(I_t,X_t)$$ with state space $$E \times \mathbb{R}^d$$, $$E$$ finite, and $$dX_t(\omega)/dt=v(i,X_ (\omega))$$, given $$I_t (\omega)=i$$. The marginal distribution of the process at time $$t$$ is shown to be the unique measure solution of a set of integro-differential equations which may be viewed as a weak form of the Chapman-Kolmogorov equation.

### MSC:

 60K10 Applications of renewal theory (reliability, demand theory, etc.) 60J25 Continuous-time Markov processes on general state spaces 93Exx Stochastic systems and control
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### References:

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