Storage impulsive processes on increasing time intervals

A storage impulsive process $S(t)$ is a sum of (jointly independent) random variables defined on the embedded Markov chain of a homogeneous Markov process.

A storage impulsive process is considered in the scheme of series on increasing time intervals $t/\varepsilon$, with a small parameter $\varepsilon \to 0$, $\varepsilon >0$. A storage impulsive process is investigated in the average and diffusion approximation scheme. The large deviation problem is considered under a corresponding scaling with an asymptotically small diffusion.