Аннотация:
We consider a time-homogeneous Markov process on discret set of states known as Weiss (simple) epidemic process. For exponential (double) generating function of the transition probabilities we consider system of first and second Kolmogorov equations. The system exact solution was obtained by using Lie group methods. We also discuss the opportunity of using the same method in the case of general epidemic process.
Ключевые слова:Markov process, exponential (double) generating function, first and second Kolmogorov equation, Fourier method, simple epidemic, general epidemic, infinitesimal symmetry generator, Lie algebra.