Why Write this Book

Markov chains or processes are named after the Russian mathematician A.A.Markov (1852-1922) who introduced the concept of chain dependence and did basic pioneering work on this class of processes [1]. A Markov process is a mathematical probabilistic model that is very useful in the study of complex systems. The essence of the model is that if the initial state of a system is known, i.e. its present state, and the probabilities to move forward to other states are also given, then it is possible to predict the future state of the system ignoring its past history. In other words, past history is immaterial for predicting the future this is the key-element in Markov chains. Distinction is made between Markov processes discrete in time and space, processes discrete in space and continuous in time and processes continuous in space and time. This book is mainly concerned with processes discrete in time and space. 

Surprisingly, despite the widespread use of Markov chains in many areas of science and technology such as Polymers, Biology, Physics, Astronomy, Astrophysics, Chemistry, Operations Research, Economics, Communications, Computer Networks etc., their applications in Chemical Engineering has been relatively meager. 

A possible reason for this phenomenon might be that books containing material on this subject have been written in such a way that the simplicity of discrete Markov chains has been shadowed by the tedious mathematical derivations. This caused one to abandon the book, thus loosing a potential tool for handling his problems. In a humorous way, this situation might be demonstrated as follows. Suppose that a Chemical Engineer wishes to study Markov processes and has been suggested several books on this subject. Since the mathematics is rather complex 

The reader can observe on the right- and left-hand sides of the desk a total of twelve books on Markov processes among which are, probably, refs. [2-8, 15-18, 84]. Some support to the fact that the books are abandoned is the prominent fact that the immediate continuation of the desk is the street... and that the books are leaning on the buildings. 

There are many advantages of using the discrete Markov-chain model in Chemical Engineering, as follows. 

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