Work

Young Parabolic PDEs and the Martingale Problem for Young SDEs

Year: 2026

Type: preprint

Abstract: Under mild regularity assumptions, we prove that the martingale problem associated with the hybrid Young--Lyons--Itô differential equation admits a unique solution in the natural class of solutions satisfying Krylov-type estimates, thereby establishing probabilistic weak well-posedness. Our proof relies on an analysis of the associated Kolmogorov equations, which are Young-type parabolic PDEs with irregular coefficients. The resulting theory for such Young-type parabolic PDEs is also of independent interest.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26291

Authors: Bugini, Fabio, Coghi, Michele, Lê, Khoa, Ling, Chengcheng

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

OpenAlex ID: W7223006460

Cites: 12

Cited by: 1

Related to: 10