Publication

C<sup>0,1</sup>-ito Chain Rules and Generalized Solutions of Parabolic Pdes

Carlo Ciccarella
2025

Abstract

In this paper, we first establish an Ito formula for a finite quadratic variation process X expanding f(t,X-t), when f is of class C-2 in space and is absolutely continuous in time. Second, via a Fukushima-Dirichlet decomposition we obtain an explicit chain rule for f(t,X-t), when X is a continuous semimartingale and f 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.

Official source

https://infoscience.epfl.ch/entities/publication/5b9e7f73-1063-41b4-8413-ffe104ace51f

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C<sup>0,1</sup>-ito Chain Rules and Generalized Solutions of Parabolic Pdes

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