Infinitesimal generator (stochastic processes)In mathematics — specifically, in stochastic analysis — the infinitesimal generator of a Feller process (i.e. a continuous-time Markov process satisfying certain regularity conditions) is a Fourier multiplier operator that encodes a great deal of information about the process. The generator is used in evolution equations such as the Kolmogorov backward equation, which describes the evolution of statistics of the process; its L2 Hermitian adjoint is used in evolution equations such as the Fokker–Planck equation, also known as Kolmogorov forward equation, which describes the evolution of the probability density functions of the process.
Random graphIn 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. The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used to answer questions about the properties of typical graphs.
Abraham de MoivreAbraham de Moivre FRS (abʁaam də mwavʁ; 26 May 1667 - 27 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He moved to England at a young age due to the religious persecution of Huguenots in France which reached a climax in 1685 with the Edict of Fontainebleau. He was a friend of Isaac Newton, Edmond Halley, and James Stirling.
Asymptotic equipartition propertyIn information theory, the asymptotic equipartition property (AEP) is a general property of the output samples of a stochastic source. It is fundamental to the concept of typical set used in theories of data compression. Roughly speaking, the theorem states that although there are many series of results that may be produced by a random process, the one actually produced is most probably from a loosely defined set of outcomes that all have approximately the same chance of being the one actually realized.
