It depends on how many elements/states of the system are put into the modeling, what  the preliminary information about the mutual influence of the states between the elements andt their states are to be considered, what the outer conditions influence the evolution of the states of single elements, etc. For generalities, any book on random (stochastic) processes might be useful, however from the question a suggestion follows, that probably some theory of semi-Markov processes were useful, if the evolution is non-Markovian and the number of states is not to high.  A pretty wide fashion of such processes with applications is given in the monograph

Semi-Markov Processes: Applications in System Reliability and Maintenance, by F. Grabski:

http://www.sciencedirect.com/science/book/9780128005187

for introduction, one can read  free available

http://www.amw.gdynia.pl/library/File/ZeszytyNaukowe/2016/ZN%20AMW_2016_3/Grabski.pdf

Also other works can be found via MrGoogle under key words:

semi markov maintenance processes   /  semi markov social sciences  /  semi markov economy markets

e.g. Semi-Markov Risk Models for Finance, Insurance and Reliability

Authors: Jacques Janssen,Raimondo Manca

for introduction to some problems one can reach free available from RG work by the authors et al.:

https://www.researchgate.net/publication/280730795_Homogeneous_Discrete_Time_Alternating_Compound_Renewal_Process_A_Disability_Insurance_Application?_iepl%5BviewId%5D=CEd3JuAJS2ig9HT1ncgqYdsD&_iepl%5BprofilePublicationItemVariant%5D=default&_iepl%5Bcontexts%5D%5B0%5D=prfpi&_iepl%5BinteractionType%5D=publicationTitle

Regards

Article Homogeneous Discrete Time Alternating Compound Renewal Proce...

well, the more one knows before?

... the more he/she uderstands later:)