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What is Absorbing Markov Chain (AMC)

Handbook of Research on Applied AI for International Business and Marketing Applications
A state of a MC is called absorbing if, once entered, it cannot be left and a MC is said to be an AMC if it has at least one absorbing state and if from every state it is possible to reach an absorbing state, not necessarily in one step. Working with an AMC one brings its transition matrix to its canonical (or standard) form by listing the absorbing states first and.with the help of it calculates its fundamental matrix, the entries of which give the mean number of steps before the absorption when the chain starts from anyone of its non-absorbing states.
Published in Chapter:
Use of Finite Markov Chains in Business Problems Involving Decision Making and Case-Based Reasoning
Michael Voskoglou (Graduate Technological Educational Institute of Western Greece, Greece)
DOI: 10.4018/978-1-7998-5077-9.ch016
Artificial intelligence (AI) is the branch of computer science focusing on the creation of intelligent machines that mimic human reasoning and behaviour. Probability theory is among the mathematical tools used in AI applications to deal with situations of uncertainty caused by randomness. In particular, the Markov chain (MC) theory is a smart combination of probability and linear algebra that offers ideal conditions for modelling such situations. International business is about the trade of goods, services, technology, capital, and knowledge at a global level, while decision making (DM) and case-based reasoning (CBR) are among the processes that are frequently used in this field. In this chapter, an absorbing and an ergodic MC model are developed on the steps of DM and CBR respectively for representing mathematically those two processes, thus providing valuable information about their evolution. The examples presented are connected to international business applications.
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