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An example of a non-Markovian process with a Markovian representation is an autoregressive time ... second-order Markov effects may also play a role in the growth of ...
Suppose that one starts with $10, and one wagers $1 on an unending, fair, coin toss indefinitely, or until all of the money is lost. If represents the number of dollars one has after n tosses, with =, then the sequence {:} is a Markov process. If one knows that one has $12 now, then it would be expected that with even odds, one will either have ...
Gauss–Markov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes. [1] [2] A stationary Gauss–Markov process is unique [citation needed] up to rescaling; such a process is also known as an Ornstein–Uhlenbeck process.
A Markov chain is a type of Markov process that has either discrete state space or discrete index set (often representing time), but the precise definition of a Markov chain varies. [196] For example, it is common to define a Markov chain as a Markov process in either discrete or continuous time with a countable state space (thus regardless of ...
The Markov-modulated Poisson process or MMPP where m Poisson processes are switched between by an underlying continuous-time Markov chain. [8] If each of the m Poisson processes has rate λ i and the modulating continuous-time Markov has m × m transition rate matrix R , then the MAP representation is
The "Markov" in "Markov decision process" refers to the underlying structure of state transitions that still follow the Markov property. The process is called a "decision process" because it involves making decisions that influence these state transitions, extending the concept of a Markov chain into the realm of decision-making under uncertainty.
A Markov decision process is a Markov chain in which state transitions depend on the current state and an action vector that is applied to the system. Typically, a Markov decision process is used to compute a policy of actions that will maximize some utility with respect to expected rewards.
The second part of the book includes many more examples in which this theory has been applied, including the Glauber dynamics on the Ising model, Markov models of chromosomal rearrangement, the asymmetric simple exclusion process in which particles randomly jump to unoccupied adjacent spaces, and random walks in the lamplighter group. [6]