Random Field

A random field is a generalization of a stochastic process such that the underlying parameter need no longer be a simple real or integer valued "time", but can instead take values that are multidimensional vectors, or points on some manifold.

At its most basic, discrete case, a random field is a list of random numbers whose indices are mapped onto a space (of n dimensions). Values in a random field are usually spatially correlated in one way or another. In its most basic form this might mean that adjacent values (i.e. values with adjacent indices) do not differ as much as values that are further apart. This is an example of a covariance structure, many different types of which may be modeled in a random field. More generally, the values might be defined over a continuous domain, and the random field might be thought of as a "function valued" random variable.

Read more about Random FieldDefinition and Examples, Applications

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... process Branching process Branching random walk Brownian bridge Brownian motion Chinese restaurant process CIR process Continuous stochastic process ... theorem Lévy process Local time (mathematics) Loop-erased random walk Markov processes are those in which the future is conditionally independent of the past given the present ... Ornstein–Uhlenbeck process Point processes random arrangements of points in a space ...
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Random Field - Applications
... Random fields are of great use in studying natural processes by the Monte Carlo method, in which the random fields correspond to naturally spatially varying properties, such as soil permeability over the ... A further common use of random fields is in the generation of computer graphics, particularly those that mimic natural surfaces such as water and earth ...

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