Search results
Results from the WOW.Com Content Network
A second-order Markov chain can be introduced by considering the current state and also the previous state, as indicated in the second table. Higher, n th-order chains tend to "group" particular notes together, while 'breaking off' into other patterns and sequences occasionally.
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.
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]
In the mathematical theory of stochastic processes, variable-order Markov (VOM) models are an important class of models that extend the well known Markov chain models. In contrast to the Markov chain models, where each random variable in a sequence with a Markov property depends on a fixed number of random variables, in VOM models this number of conditioning random variables may vary based on ...
If a stochastic process is N-th-order stationary, then it is also M-th-order stationary for all . If a stochastic process is second order stationary (=) and has finite second moments, then it is also wide-sense stationary. [1]: p. 159
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.
A master equation is a phenomenological set of first-order ... the second subscript the column. ... this identifies the evolution as a continuous-time Markov process, ...
A Markov arrival process is defined by two matrices, D 0 and D 1 where elements of D 0 represent hidden transitions and elements of D 1 observable transitions. The block matrix Q below is a transition rate matrix for a continuous-time Markov chain.