[2210.13530] An efficient Monte Carlo scheme for Zakai equations
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:2210.13530 (math)
[Submitted on 24 Oct 2022 (v1), last revised 21 Aug 2023 (this version, v2)]

Title:An efficient Monte Carlo scheme for Zakai equations

Authors:Christian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, Ariel Neufeld
View PDF
Abstract:In this paper we develop a numerical method for efficiently approximating solutions of certain Zakai equations in high dimensions. The key idea is to transform a given Zakai SPDE into a PDE with random coefficients. We show that under suitable regularity assumptions on the coefficients of the Zakai equation, the corresponding random PDE admits a solution random field which, for almost all realizations of the random coefficients, can be written as a classical solution of a linear parabolic PDE. This makes it possible to apply the Feynman--Kac formula to obtain an efficient Monte Carlo scheme for computing approximate solutions of Zakai equations. The approach achieves good results in up to 25 dimensions with fast run times.
Subjects: Numerical Analysis (math.NA); Probability (math.PR); Computation (stat.CO)
MSC classes: 65C05, 65M75, 60H15, 62M20
Cite as: arXiv:2210.13530 [math.NA]
  (or arXiv:2210.13530v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2210.13530
Related DOI: https://doi.org/10.1016/j.cnsns.2023.107438

Submission history

From: Ariel Neufeld [view email]
[v1] Mon, 24 Oct 2022 18:32:51 UTC (2,230 KB)
[v2] Mon, 21 Aug 2023 02:53:16 UTC (972 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.NA
< prev   |   next >
new | recent | 2022-10
Change to browse by:
cs
cs.NA
math
math.PR
stat
stat.CO

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?)