Time Dependent Tempered Generalized Functions and Ito's Formula

2010/07/04 by Pedro Catuogno, P. Catuogno, Catuogno, P. +3
Computer Science · Mathematics · #46F10 #60H99 #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical and Theoretical Analysis #Numerical Methods and Algorithms #Probability (math.PR) #math.FA #math.PR #msc:46F10 #msc:60H99

paper · pdf · doi:10.48550/arxiv.1007.0564

18 pages

openalex publication_date 2010/07/04 · arxiv created 2011/11/08 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Itô's formula for Lévy-Itô processes taking values in the dual of nuclear space

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