Convergence Rates for the Quantum Central Limit Theorem

Convergence rates for the central limit theorem.

Rates of convergence for minimal distances in the central limit theorem under projective criteria

In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying projective criteria. Applications to functions of linear processes and to functions of expanding maps of the interval are given.

The Edgeworth Expansion and Convergence in the Central Limit Theorem

For regularity of φ, proceed by induction, write the derivative difference quotient, use the mean value theorem on the corresponding integrand and apply LDCT. • Corollary 1 If X has m finite moment and law μ, then φ(ξ) = ∫ R e (ix)dμ(x) for k ≤ m. • Theorem 2 If S = ∑n k=1 Xk where {Xk} are independent with c.f.’s φk the c.f. of S, φ satisfies φ = ∏n k=1 φk. Proof: The law of S is the n-fold co...

A Tracial Quantum Central Limit Theorem

We prove a central limit theorem for non-commutative random variables in a von Neumann algebra with a tracial state: Any non-commutative polynomial of averages of i.i.d. samples converges to a classical limit. The proof is based on a central limit theorem for ordered joint distributions together with a commutator estimate related to the Baker-Campbell-Hausdorff expansion. The result can be cons...

Mcmc Convergence Diagnostic via the Central Limit Theorem

Markov Chain Monte Carlo (MCMC) methods, as introduced by Gelfand and Smith (1990), provide a simulation based strategy for statistical inference. The application elds related to these methods, as well as theoretical convergence properties, have been intensively studied in the recent literature. However, many improvements are still expected to provide workable and theoretically well-grounded so...