One way of interpreting the convergence of a sequence Xn to X is to say that the ''distance'' between X and Xn is getting smaller and smaller.

In measure theory, Lebesgue's dominated convergence theorem gives a mild sufficient condition under which limits and integrals of a sequence of functions ... Statement · Proof · Bounded convergence theorem

Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability · Abstract · Keywords.

This lecture discusses mean-square convergence, first for sequences of random variables and then for sequences of random vectors. The formula that defines ...

Convergence in mean · When Xn converges in r-th mean to X for r = 1, we say that Xn converges in mean to X. · When Xn converges in r-th mean to X for r = 2, we ... Convergence of measures · Proofs · Fatou's lemma · Borel–Cantelli lemma

6 дек. 2012 г. · A version of the fundamental mean-square convergence theorem is proved for stochastic differential equations (SDE) which coefficients are allowed to grow ...

The mean convergence theorem is proved assuming that {‖Vnj‖r, 1⩽j⩽kn, n⩾1} is {|anj|r}-uniformly integrable whereas the weak law is proved under a Cesàro type ...

A version of the fundamental mean-square convergence theorem is proved for stochas- tic differential equations (SDEs) in which coefficients are allowed to ...

14 дек. 2020 г. · Convergence in probability implies convergence in distribution, and together with Skorokhod's theorem, this implies E[Xn]→E[X], but I don't ...

The Baillon-type nonlinear mean convergence theorem for finite commutative generic 2-generalized Bregman nonspreading mappings without the convexity assumption ...