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:2210.01334 (math)
[Submitted on 4 Oct 2022 (v1), last revised 25 May 2023 (this version, v2)]

Title:Averaging principle for slow-fast systems of rough differential equations via controlled paths

Authors:Yuzuru Inahama
View PDF
Abstract:In this paper we prove the strong averaging principle for a slow-fast system of rough differential equations. The slow and the fast component of the system are driven by a rather general random rough path and Brownian rough path, respectively. These two driving noises are assumed to be independent. A prominent example of the driver of the slow component is fractional Brownian rough path with Hurst parameter between 1/3 and 1/2. We work in the framework of controlled path theory, which is one of the most widely-used frameworks in rough path theory. To prove our main theorem, we carry out Khas'minskii's time-discretizing method in this framework.
Comments: 44 pages, no figure
Subjects: Probability (math.PR); Dynamical Systems (math.DS)
MSC classes: 60L90 (Primary) 70K65, 70K70, 60F99 (Secondary)
Cite as: arXiv:2210.01334 [math.PR]
  (or arXiv:2210.01334v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.2210.01334

Submission history

From: Yuzuru Inahama [view email]
[v1] Tue, 4 Oct 2022 02:59:49 UTC (39 KB)
[v2] Thu, 25 May 2023 07:49:03 UTC (40 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
license icon view license
Current browse context:
math.PR
< prev   |   next >
new | recent | 2022-10
Change to browse by:
math
math.DS

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?)