Pith. sign in

REVIEW 1 cited by

Asymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/0503601 v1 pith:CBT2REIB submitted 2005-03-25 math.PR

classification math.PR
keywords asymptoticbanachfieldsprobabrandomrelatedtheoryvariables
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

Let X_i, i\in N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let \Phi be a smooth enough mapping from B into R. An asymptotic evaluation of Z_n=E(\exp (n\Phi (\sum_{i=1}^nX_i/n))), up to a factor (1+o(1)), has been gotten in Bolthausen [Probab. Theory Related Fields 72 (1986) 305-318] and Kusuoka and Liang [Probab. Theory Related Fields 116 (2000) 221-238]. In this paper, a detailed asymptotic expansion of Z_n as n\to \infty is given, valid to all orders, and with control on remainders. The results are new even in finite dimensions.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Shared Observation Shields Collective Fluctuations while Preserving Local Independence

    cond-mat.stat-mech 2026-08 conditional novelty 6.0 of 10

    Conditioning an exchangeable population on its own noisy collective record produces a rank-one, nonpositive Schur shield correction to collective fluctuations while keeping pair correlations at O(1/z), giving a calcul...

Pith tools