  The acquisition of charge by aerosol particles is well-known to be stochastic
in nature. We review the principles of charging using the conceptually and
computationally clear language of continuous time Markov processes. A novel
numeric approach is presented that can be used to calculate the time evolution
of various particle charging processes. Its modular character makes it easy to
implement and allows for quick adaptation to specific problems. We conclude
with the application of ergodicity for finite state-space Markov processes in
order to determine stationary charge distributions in case of bipolar charging.
