Time Dependent Tempered Generalized Functions and Ito's Formula
P. Catuogno, C. Olivera
TL;DR
This paper develops a new Ito's formula for time-dependent tempered generalized functions and applies it to the heat equation with generalized initial conditions, also providing a new proof of Ustunel-Ito's formula.
Contribution
It introduces a novel Ito's formula for time-dependent tempered generalized functions and extends its application to generalized initial conditions in the heat equation.
Findings
New Ito's formula for time-dependent tempered generalized functions
Application to heat equation with generalized initial conditions
Alternative proof of Ustunel-Ito's formula
Abstract
The paper introduces a novel Ito's formula for time dependent tempered generalized functions. As an application, we study the heat equation when initial conditions are allowed to be a generalized tempered function. A new proof of the Ustunel- Ito's formula for tempered distributions is also provided.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical and Theoretical Analysis · Numerical Methods and Algorithms · Functional Equations Stability Results