Translation and analysis of words by artificial intelligence
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homogeneous$35683$ - translation to italian
![Wiener]] or [[Brownian motion]] process on the surface of a sphere. The Wiener process is widely considered the most studied and central stochastic process in probability theory.<ref name="doob1953stochasticP46to47"/><ref name="RogersWilliams2000page1"/><ref name="Steele2012page29"/>](https://commons.wikimedia.org/wiki/Special:FilePath/BMonSphere.jpg?width=200 "Wiener]] or [[Brownian motion]] process on the surface of a sphere. The Wiener process is widely considered the most studied and central stochastic process in probability theory.<ref name=\"doob1953stochasticP46to47\"/><ref name=\"RogersWilliams2000page1\"/><ref name=\"Steele2012page29\"/>")
![Mathematician [[Joseph Doob]] did early work on the theory of stochastic processes, making fundamental contributions, particularly in the theory of martingales.<ref name="Getoor2009"/><ref name="Snell2005"/> His book ''Stochastic Processes'' is considered highly influential in the field of probability theory.<ref name="Bingham2005"/>](https://commons.wikimedia.org/wiki/Special:FilePath/Joseph Doob.jpg?width=200 "Mathematician [[Joseph Doob]] did early work on the theory of stochastic processes, making fundamental contributions, particularly in the theory of martingales.<ref name=\"Getoor2009\"/><ref name=\"Snell2005\"/> His book ''Stochastic Processes'' is considered highly influential in the field of probability theory.<ref name=\"Bingham2005\"/>")
Definition
Wikipedia
In physics, a homogeneous material or system has the same properties at every point; it is uniform without irregularities. A uniform electric field (which has the same strength and the same direction at each point) would be compatible with homogeneity (all points experience the same physics). A material constructed with different constituents can be described as effectively homogeneous in the electromagnetic materials domain, when interacting with a directed radiation field (light, microwave frequencies, etc.).
Mathematically, homogeneity has the connotation of invariance, as all components of the equation have the same degree of value whether or not each of these components are scaled to different values, for example, by multiplication or addition. Cumulative distribution fits this description. "The state of having identical cumulative distribution function or values".
