Work

C0,1-Itô chain rules and generalized solutions of parabolic PDEs

Year: 2025

Type: article

Abstract: In this paper, we first establish an Itô formula for a finite quadratic variation process [Formula: see text] expanding [Formula: see text] when [Formula: see text] is of class [Formula: see text] in space and is absolutely continuous in time. Second, via a Fukushima–Dirichlet decomposition we obtain an explicit chain rule for [Formula: see text], when [Formula: see text] is a continuous semimartingale and [Formula: see text] is a “quasi-strong solution” (in the sense of approximation of classical solutions) of a parabolic PDE. Those results are applied in a companion paper to establish a verification theorem in stochastic differential games.

Source: Stochastics and Dynamics

DOI: 10.1142/s0219493725500194

Authors: Carlo Ciccarella, Francesco Russo

Institutions: École Polytechnique Fédérale de Lausanne, École Nationale Supérieure de Techniques Avancées, Institut Polytechnique de Paris, École Nationale Supérieure de Techniques Avancées Paris, Unité de Mathématiques Appliquées

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: Stochastic and deterministic analysis for Irregular Models.