To study special Markov processes with infinitely divisible limit distributions, the characteristic function was used.

The concept of average Markov process is introduced.

Based on the description of hybrid states and under certain assumptions, the system becomes a time-homogeneous hybrid state Markov process.

there are certain infection patients initially in one area,suppose on one hand,the patient is increasing constantly,and the infectious rate is affected by patient s figure at that time;on the other hand,emergence frequency and figure of the patient reduces (death or cures)are affected by an external environment,and the external environment assumes for a Markov processes with limited states,under.

In this paper,we are to study a strong law of large numbers for function of Markov processes and Markov chains in Markovian environments.

For the semigroup corresponding to a vector Markov process whose components are independent Markov processes, an “addition theorem” about algebraic L 2 decay is obtained.

This paper studies the relate d problems to risk models, uses the phase type semi-Markov processes to replace the finite Markov processes, same results are obtained.

In this paper,reinforcement learning and semi-Markov process are applied to inventory control of supply chain management ranged among regions with different production costs.