Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Probability

arXiv:2201.12797 (math)
[Submitted on 30 Jan 2022 (v1), last revised 16 Aug 2022 (this version, v3)]

Title:Wasserstein Convergence Rates for Empirical Measures of Subordinated Processes on Noncompact Manifolds

Authors:Huaiqian Li, Bingyao Wu
View PDF
Abstract:The asymptotic behaviour of empirical measures has been studied extensively. In this paper, we consider empirical measures of given subordinated processes on complete (not necessarily compact) and connected Riemannian manifolds with possibly nonempty boundary. We obtain rates of convergence for empirical measures to the invariant measure of the subordinated process under the Wasserstein distance. The results, established for more general subordinated processes than [arXiv:2107.11568], generalize the recent ones in [Stoch. Proc. Appl. 144(2022), 271--287] and are shown to be sharp by a typical example. The proof is motivated by the aforementioned works.
Subjects: Probability (math.PR)
Cite as: arXiv:2201.12797 [math.PR]
  (or arXiv:2201.12797v3 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.2201.12797

Submission history

From: Huaiqian Li [view email]
[v1] Sun, 30 Jan 2022 12:18:57 UTC (19 KB)
[v2] Sat, 30 Jul 2022 13:57:32 UTC (20 KB)
[v3] Tue, 16 Aug 2022 10:59:06 UTC (20 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.PR
< prev   |   next >
new | recent | 2022-01
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)