Rates of Weak Convergence and Asymptotic Expansions for Classical Central Limit Theorems

Asymptotic Expansions in Free Limit Theorems

We study asymptotic expansions in free probability. In a class of classical limit theorems Edgeworth expansion can be obtained via a general approach using sequences of “influence” functions of individual random elements described by vectors of real parameters (ε1, . . . , εn), that is by a sequence of functions hn(ε1, . . . , εn; t), |εj | ≤ 1 n , j = 1, . . . , n, t ∈ A ⊂ R (or C) which are s...

A.D.Wentzell (Tulane University) Limit theorems with asymptotic expansions for stochastic processes. There is a vast riches of limit theorems for sums of independent random variables: theorems about weak convergence, on large deviations, theorems with asymptotic expan-

There is a vast riches of limit theorems for sums of independent random variables: theorems about weak convergence, on large deviations, theorems with asymptotic expansions, etc. We can try to obtain the same kinds of theorems for families of stochastic processes. If X1, X2, ..., Xn, ... is a sequence of independent identically distributed random variables with expectation EXi = 0 and variance ...

Convergence rates for the central limit theorem.

Rates of Convergence for Central Limit Theorems for Random Walks Related with the Hankel Transform

Pointwise convergence rates and central limit theorems for kernel density estimators in linear processes

Convergence rates and central limit theorems for kernel estimators of the stationary density of a linear process have been obtained under the assumption that the innovation density is smooth (Lipschitz). We show that smoothness is not required. For example, it suffices that the innovation density has bounded variation.