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

representation theorem In probability theory Hahn–Kolmogorov theorem Kolmogorov extension theorem Kolmogorov continuity theorem Kolmogorov's three-series theorem Kolmogorov's...

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

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...

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

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

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

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...

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

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

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

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...

[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...

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

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

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...

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

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

{\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...

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

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

{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)...

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

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...

they are groups and topological spaces at the same time, such that the continuity condition for the group operations connects these two structures together...

origin. Normability of topological vector spaces is characterized by Kolmogorov's normability criterion. A TVS is seminormable if and only if it has a...