![]() The main idea is that individuals can be classified into three states: Susceptible (people that can get the disease), Infected (people that have the disease and are contagious), and Removed. The most famous is the SIR model for infectious diseases. The Markov Chains are usually called in the epidemiological and in the chemistry literature “compartmental models”. Other areas of application include predicting asset and option prices and calculating credit risks. In economics and finance, they are often used to predict macroeconomic situations like market crashes and cycles between recession and expansion. These fields range from the mapping of animal life populations to search engine algorithms, music composition and speech recognition. Since Markov chains can be designed to model many real-world processes, they are used in a wide variety of situations. However, an infinite-state Markov chain does not have to be a steady-state, but a steady-state Markov chain must be time-homogenous. This phenomenon is also called a steady-state Markov chain where the probabilities for different outcomes converge to a certain value. ![]() A continuous-time Markov chain changes at any time.Ī Markov chain can be stationary and therefore be independent of the initial state in the process. The value of the Markov chain in discrete-time is called the state and in this case, the state corresponds to the closing price. One example to explain the discrete-time Markov chain is the price of an asset where the value is registered only at the end of the day. In this article, we will focus on discrete-time Markov chains. This means that we have one case where the changes happen at specific states and one where the changes are continuous. When approaching Markov chains there are two different types: discrete-time Markov chains and continuous-time Markov chains.
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