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

Mathematics > Numerical Analysis

arXiv:1301.5389 (math)
[Submitted on 23 Jan 2013 (v1), last revised 19 Jan 2014 (this version, v2)]

Title:Stability of analytical and numerical solutions of nonlinear stochastic delay differential equations

Authors:Siqing Gan, Aiguo Xiao, Desheng Wang
View PDF
Abstract:This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean square of the solutions for nonlinear SDDEs. The results provide a unified theoretical treatment for SDDEs with constant delay and variable delay (including bounded and unbounded variable delays). Then the stability, contractivity and asymptotic contractivity in mean square are investigated for the backward Euler method. It is shown that the backward Euler method preserves the properties of the underlying SDDEs. The main results obtained in this work are different from those of Razumikhin-type theorems. Indeed, our results hold without the necessity of constructing of finding an appropriate Lyapunov functional.
Comments: 23 pages
Subjects: Numerical Analysis (math.NA)
MSC classes: 34K50, 65C20, 65C30
Cite as: arXiv:1301.5389 [math.NA]
  (or arXiv:1301.5389v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1301.5389

Submission history

From: Siqing Gan [view email]
[v1] Wed, 23 Jan 2013 02:58:35 UTC (19 KB)
[v2] Sun, 19 Jan 2014 14:47:59 UTC (19 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.NA
< prev   |   next >
new | recent | 2013-01
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?)