I research the Mathematical Chemical Reaction Network Theory(CRNT).
Chemical reaction network is the basic structure of mutual interacting of molecules(species) such as 2H + O <-> H2O. When finitely many combinations(complex) of chemical molecules communicate each other, chemists and biologist are interested in how their concentration vary in time. When the total number of molecules (total mass) in the chemical reaction is huge enough, then we can assume the concentration of each molecule is continuously varying. So that it is governed by ordinary differential equation provided there is no spatial difference. We say this case is called deterministic case. If the total number of molecules is relatively small, otherwise, then we will observe the chemical reaction by stochastic sense. This case is called stochastic case.
I mainly focus on the stochastic CRNT. In this model, reactions between molecules does not occur at almost time but only occur at specific time. Therefore molecule's concentrations can be represented with Continuous Time Poisson Jump Process. That is, their reactions happen at specific time with specific probabilities. Recently, what I am interested in is ; which initial distributions makes the distribution of concentration of molecules stationary??, even such initial distributions exist??