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A basic property about an absorbing Markov chain is the expected number of visits to a transient state j starting from a transient state i (before being absorbed). This can be established to be given by the (i, j) entry of so-called fundamental matrix N, obtained by summing Q k for all k (from 0 to ∞).
A finite-state machine can be used as a representation of a Markov chain. Assuming a sequence of independent and identically distributed input signals (for example, symbols from a binary alphabet chosen by coin tosses), if the machine is in state y at time n, then the probability that it moves to state x at time n + 1 depends only on the ...
A Markov chain is a type of Markov process that has either a discrete state space or a discrete index set (often representing time), but the precise definition of a Markov chain varies. [6] 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 ...
The sequence in which each of the phases occur may itself be a stochastic process. The distribution can be represented by a random variable describing the time until absorption of an absorbing Markov chain with one absorbing state. Each of the states of the Markov chain represents one of the phases.
Markov chain; Markov chain central limit theorem; Markov chain geostatistics; Markov chain Monte Carlo; Markov partition; Markov property; Markov switching multifractal; Markovian discrimination; Maximum-entropy Markov model; MegaHAL; Models of DNA evolution; MRF optimization via dual decomposition; Multiple sequence alignment
Nucleic acids consist of a chain of linked units called nucleotides. Each nucleotide consists of three subunits: a phosphate group and a sugar (ribose in the case of RNA, deoxyribose in DNA) make up the backbone of the nucleic acid strand, and attached to the sugar is one of a set of nucleobases.
In probability a quasi-stationary distribution is a random process that admits one or several absorbing states that are reached almost surely, but is initially distributed such that it can evolve for a long time without reaching it. The most common example is the evolution of a population: the only equilibrium is when there is no one left, but ...
This category is for articles about the theory of Markov chains and processes, and associated processes. See Category:Markov models for models for specific applications that make use of Markov processes.