Data Science: Markov Process (Definitions)

"A Markov process is any stochastic process in which the future development is completely determined by the present state and not at all by the way in which the present state arose." (David B MacNeil, "Modern Mathematics for the Practical Man", 1963)

"A Markov process is a stochastic process in which present events depend on the past only through some finite number of generations. In a first-order Markov process, the influential past is limited to a single earlier generation: the present can be fully accounted for by the immediate past." (Manfred Schroeder, "Fractals, Chaos, Power Laws Minutes from an Infinite Paradise", 1990)

"stochastic process in which the new state of a system depends on the previous state only (or more generally, on a finite set of previous states)." (Teuvo Kohonen, "Self-Organizing Maps" 3rd Ed., 2001)

"A stochastic process in which the transition probabilities can be estimated on the basis of first order data. Such a process is also stationary in that probability estimates do not change across the sample (generally across time)." (W David Penniman,"Historic Perspective of Log Analysis", 2009)

"Stochastic process in which the new state of a system depends on the previous state or a finite set of previous states." (Patrick Rousset & Jean-Francois Giret, "A Longitudinal Analysis of Labour Market Data with SOM" Encyclopedia of Artificial Intelligence, 2009)

"A stochastic process where the probabilities of the events depend on the previous event only." (Michael M Richter, "Business Processes, Dynamic Contexts, Learning", 2014)

"A Markov chain (or Markov process) is a system containing a finite number of distinct states S1,S2,…,Sn on which steps are performed such that: (1) At any time, each element of the system resides in exactly one of the states. (2) At each step in the process, elements in the system can move from one state to another. (3) The probabilities of moving from state to state are fixed - that is, they are the same at each step in the process." (Stephen Andrilli & David Hecker, [in [Elementary Linear Algebra] 5th Ed.), 2016)

[hidden Markov model:] "A hidden Markov model is a technique for modeling sequences using a hidden state that only uses the previous part of the sequence." (Alex Thomas, "Natural Language Processing with Spark NLP", 2020)

[Markov decision process:] "A stochastic dynamic program, whereby for each policy the resulting state variables comprise a Markov process (a stochastic process with the property that the conditional probability of a transition to any state depends only on the current state, and not on previous states)." (Mathematical Programming Glossary)