Weak Convergence Rates for Partial-Sum Processes of Nonlinear Stochastic Approximation K5H6GS0SGQ

URI	`m2://res/K5H6GS0SGQ`
Kind	preprint
Creators	Xiang Li, Jiadong Liang, Zhihua Zhang
Date	2026-09-30
MSC	62-XX
Subjects	arxiv math.ST, arxiv stat.TH
Scope	in

Expressions

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
Quantitative recursion coefficients	statement	lemma 4.9	arxiv
A nonlinear obstruction under a trajectory moment bound	statement	theorem 3.6	arxiv
Brownian tail bound	statement	lemma 4.6	arxiv
Stochastic oracle	definition	definition 3.2	arxiv
Subquadratic BDG maximal inequality	statement	lemma 4.4	arxiv
Probability-radius calculus	statement	lemma 4.1	arxiv
Scott--Huggins martingale embedding	statement	lemma 4.5	arxiv
Qualitative FCLT for the Polyak--Ruppert trajectory	statement	theorem 2.1	arxiv
Two-regime tail-to-radius conversion	statement	lemma 4.3	arxiv
Adaptive-block maximal inequality	statement	lemma 4.10	arxiv
Maximal martingale Fuk--Nagaev inequality	statement	lemma 4.2	arxiv
Sharpness of the conditional-covariance-stabilization exponent	statement	theorem 3.3	arxiv
\(J_1\) Skorokhod metric	definition	definition 2.2	arxiv
Normalized martingale functional approximation	statement	lemma 4.11	arxiv
Power-law contraction-sum estimates	statement	lemma 4.7	arxiv
Sharp intrinsic rate in the scalar Gaussian model	statement	theorem 3.5	arxiv
Prokhorov distance	definition	definition 2.3	arxiv
Deterministic power-law step-size bounds	statement	lemma 4.8	arxiv
Worst-case finite-moment lower bound for linear SA	statement	theorem 3.4	arxiv
Quantitative functional CLT for fixed projections of nonlinear SA	statement	theorem 3.1	arxiv
Overall lower bound for the full SA path	statement	theorem 3.7	arxiv