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This random process finds wide application in model building: In physics , spin systems and fluorescence intermittency show dichotomous properties. But especially in single molecule experiments probability distributions featuring algebraic tails are used instead of the exponential distribution implied in all formulas above.
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 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 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.
Statistical signal processing is an approach which treats signals as stochastic processes, utilizing their statistical properties to perform signal processing tasks. [11] Statistical techniques are widely used in signal processing applications.
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.