Kantorovich considered infinite-dimensional optimization problems, such as the Kantorovich-Monge problem in weak convergence of probability measures.
12.
The discussion is mainly based on the book " Weak Convergence and Empirical Processes : With Applications to Statistics ".
13.
There are several equivalent definitions of weak convergence of a sequence of measures, some of which are ( apparently ) more general than others.
14.
His research interests also include measure-theoretical analysis, weak convergence methods, stochastic partial differential equations, statistical physics, and numerical analysis.
15.
*( see p . 7 for weak convergence, p . 24 for convergence in distribution and p . 70 for Skorokhod's theorem)
16.
The terms are uniformly bounded in L p, so to check weak convergence to 0 it enough to check inner products with a dense subset of L 2.
17.
For instance, stochastic equicontinuity, along with other conditions, can be used to show uniform weak convergence, which can be used to prove the convergence of extremum estimators.
18.
Furthermore, convergence with respect to " W " " p " is equivalent to the usual weak convergence of measures plus convergence of the first " p " th moments.
19.
More generally, if the u . a . n . condition is satisfied via a scaling of identically distributed random variables ( with not necessarily finite second moment ), then the weak convergence is to a stable distribution.
20.
The Delta-compactness theorem is similar to the Banach Alaoglu theorem for weak convergence but, unlike the Banach-Alaoglu theorem ( in the non-separable case ) its proof does not depend on the Axiom of Choice.
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