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It models burst noise (also called popcorn noise or random telegraph signal). If the two possible values that a random variable can take are c 1 {\displaystyle c_{1}} and c 2 {\displaystyle c_{2}} , then the process can be described by the following master equations :
It is also called random telegraph noise (RTN), popcorn noise, impulse noise, bi-stable noise, or random telegraph signal (RTS) noise. It consists of sudden step-like transitions between two or more discrete voltage or current levels, as high as several hundred microvolts , at random and unpredictable times.
Point processes: random arrangements of points in a space . They can be modelled as stochastic processes where the domain is a sufficiently large family of subsets of S , ordered by inclusion; the range is the set of natural numbers; and, if A is a subset of B , ƒ ( A ) ≤ ƒ ( B ) with probability 1.
In statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it can be used to describe certain time-varying processes in nature, economics, behavior, etc.
For example, processes in the AR(1) model with | | are not stationary because the root of = lies within the unit circle. [3] The augmented Dickey–Fuller test assesses the stability of IMF and trend components. For stationary time series, the ARMA model is used, while for non-stationary series, LSTM models are used to derive abstract features.
Markov random fields find application in a variety of fields, ranging from computer graphics to computer vision, machine learning or computational biology, [13] [14] and information retrieval. [15] MRFs are used in image processing to generate textures as they can be used to generate flexible and stochastic image models.
In physics and mathematics, a random field is a random function over an arbitrary domain (usually a multi-dimensional space such as ). That is, it is a function f ( x ) {\displaystyle f(x)} that takes on a random value at each point x ∈ R n {\displaystyle x\in \mathbb {R} ^{n}} (or some other domain).
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. [1] [2] The theory of random graphs lies at the intersection between graph theory and probability theory.