For dependent, approximately stationary random functions in C0, the partial sum process is within O(N^{-τ}) of a functional Brownian motion in Prokhorov and Wasserstein distance.
Wasserstein convergence rates in the invariance principle for sequential dynamical systems
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this paper, we consider the convergence rate with respect to the Wasserstein distance in the invariance principle for sequential dynamical systems. We utilize and modify the techniques previously employed for stationary sequences to address our non-stationary case. Under certain assumptions, we can apply our result to a large class of dynamical systems, including sequential $\beta_n$-transformations, piecewise uniformly expanding maps with additive noise in one-dimensional and multidimensional case, and so on.
citation-role summary
background 1
citation-polarity summary
fields
math.ST 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Prokhorov Metric Convergence of the Partial Sum Process for Reconstructed Functional Data
For dependent, approximately stationary random functions in C0, the partial sum process is within O(N^{-τ}) of a functional Brownian motion in Prokhorov and Wasserstein distance.