Definition
Consider a system, which can be described at any point of time t using a state variable Xt. This state variable may be a D-dimensional vector (where D may be 1 or higher), defined on a space X called the state space, and each individual value in the state space is called a state. This space can be either discrete or continuous, depending on the nature of the system. Time may be considered to be discrete. System dynamics refers to the process by which the state of the system changes over time, so that we have a sequence of states {X1, X2, …, Xt−1, Xt, Xt+1, …}. The changes of state from one time-point to the next are known as state transitions. If the state space is discrete and finite, we can look upon a Markov chain as a finite-state machine which shifts between the different states.
Suppose, these state variables are random variables, i.e., their values are assigned according to probability distributions. We describe such a system as a Markov chainif the state transition...
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Mitra, A. (2023). Markov Chains: Addition. In: Daya Sagar, B.S., Cheng, Q., McKinley, J., Agterberg, F. (eds) Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-85040-1_192
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DOI: https://doi.org/10.1007/978-3-030-85040-1_192
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