Markov chain in a narrow sense is a branch of stochastic process, which was put forward by Markov, a mathematician in the former Soviet Union, at the beginning of last century. Therefore, a detailed introduction to Markov chains can be found in any book Random Process.

Of course, today, the concept of Markov chain has greatly surpassed the original model. It can be said that all stochastic processes that conform to Markov properties can be studied by Markov chains. Several basic models, such as genetic process, population reproduction, Poisson flow, Brownian motion and even stochastic differential equations in stochastic analysis, can be used for financial market analysis and pricing. The concept of martingale derived from Markov property is also one of the research frontiers in the field of stochastic mathematics. In a word, the generalized Markov chain is the floorboard of a series of stochastic processes with Markov properties.

If LZ wants to know the relevant contents, he can look up some books about stochastic processes. There will be a special introduction above.

I recommend two books, The Application of Stochastic Processes, Lin and Tsinghua University Publishing House.

Two teachers of HKUST wrote it in Random Process Science Press.

The former is more comprehensive and profound, but the mathematical theory is also deeper, which is not suitable for people who are not majoring in mathematics or have a general mathematical foundation. The introduction of the latter is more direct and suitable for getting started.