In mathematics, the Kolmogorov continuity theorem is a theorem that guarantees that a stochastic process that satisfies certain constraints on the moments...

theory Hahn–Kolmogorov theorem Kolmogorov extension theorem Kolmogorov continuity theorem Kolmogorov's three-series theorem Kolmogorov's zero–one law...

case) Kolmogorov dimension (upper box dimension) Kolmogorov–Arnold theorem Kolmogorov–Arnold–Moser theorem Kolmogorov continuity theorem Kolmogorov's criterion...

variables Kolmogorov continuity theorem, on stochastic processes In geometry: Parametric continuity, for parametrised curves Geometric continuity, a concept...

the Kolmogorov extension theorem (also known as Kolmogorov existence theorem, the Kolmogorov consistency theorem or the Daniell-Kolmogorov theorem) is...

the continuity theorem may refer to one of the following results: the Lévy continuity theorem on random variables; the Kolmogorov continuity theorem on...

real analysis and approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous...

infinity. Kolmogorov strengthened this result, by effectively providing the rate of this convergence (see Kolmogorov distribution). Donsker's theorem provides...

expectation is a consequence of the Radon–Nikodym theorem. This was formulated by Kolmogorov in 1933. Kolmogorov underlines the importance of conditional probability...

In functional analysis, the Fréchet–Kolmogorov theorem (the names of Riesz or Weil are sometimes added as well) gives a necessary and sufficient condition...

meets certain moment conditions on its increments, then the Kolmogorov continuity theorem says that there exists a modification of this process that has...

[X_{k}]<\infty .} This statement is known as Kolmogorov's strong law, see e.g. Sen & Singer (1993, Theorem 2.3.10). The weak law states that for a specified...

uncertainty Kolmogorov backward equation Kolmogorov continuity theorem Kolmogorov extension theorem Kolmogorov's criterion Kolmogorov's generalized criterion...

generalized central limit theorem (GCLT) was an effort of multiple mathematicians (Bernstein, Lindeberg, Lévy, Feller, Kolmogorov, and others) over the period...

theory) Karhunen–Loève theorem (stochastic processes) Kolmogorov extension theorem (stochastic processes) Kolmogorov's three-series theorem (mathematical series)...

process is a Markov process with continuous sample paths for which the Kolmogorov forward equation is the Fokker–Planck equation. A diffusion process is...

{\displaystyle X_{t}} is also a Gaussian process. In other cases, the central limit theorem indicates that X t {\displaystyle X_{t}} will be approximately normally...

uniformly distributed random phase. Where applicable, the central limit theorem dictates that at any point, the sum of these individual plane-wave contributions...

Carleson's theorem is a fundamental result in mathematical analysis establishing the pointwise (Lebesgue) almost everywhere convergence of Fourier series...

dx=\mathbb {P} _{t+\Delta t,t'}(y\mid x'),} which is the Chapman–Kolmogorov theorem. Changing the dummy variable y {\displaystyle y} to x {\displaystyle...

directed complete partial order (dcpo) with the Scott topology is always a Kolmogorov space (i.e., it satisfies the T0 separation axiom). However, a dcpo with...

machinery can be subsequently applied. Continuity of sample paths can be shown using Kolmogorov continuity theorem. Functional data are considered as realizations...

Karhunen–Loève theorem Kolmogorov continuity theorem Kolmogorov extension theorem Lévy–Prokhorov metric Malliavin calculus Martingale representation theorem Optional...

mathematics and statistics, the quasi-arithmetic mean or generalised f-mean or Kolmogorov-Nagumo-de Finetti mean is one generalisation of the more familiar means...

martingale convergence theorems / (SU:R) Doob–Meyer decomposition theorem / (U:R) Feller-continuous process / (U:R) Kolmogorov continuity theorem / (U:R) Local...

{f}}(\xi )\right|^{2}\,d\xi .} Plancherel's theorem makes it possible to extend the Fourier transform, by a continuity argument, to a unitary operator on L2(R)...

Karhunen–Loève theorem Kolmogorov continuity theorem Kolmogorov extension theorem Lévy–Prokhorov metric Malliavin calculus Martingale representation theorem Optional...

Königsberg problem and polyhedron formula are arguably the field's first theorems. The term topology was introduced by Johann Benedict Listing in the 19th...

reduce the error in approximation, Frank Yates suggested a correction for continuity that adjusts the formula for Pearson's chi-squared test by subtracting...

and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiability and integrability. Real analysis is distinguished...