A Handbook of Mathematical Models with Python

8

Markov Chain

The Markov chain is one of the most important stochastic processes and solves real-world problems with probabilities. A Markov chain is a model of random movement in a discrete set of possible locations (states), in other words, a model of transition from one location (state) to another with a certain probability. It is named after Andrey Markov, the Russian mathematician who is best known for his work on stochastic processes. It is a mathematical system describing a sequence of events in which the probability of each event depends only on the previous event.

“The future depends only upon the present, not upon the past.”

The events or states can be written as {, where is the state at time t. The process {} has a property, which ...