On nonlinear rough paths

Nualart, David and Xia, Panqiu 2020. On nonlinear rough paths. ALEA : Latin American Journal of Probability and Mathematical Statistics 17 (1) , pp. 545-587. 10.30757/alea.v17-22

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Abstract

n this paper, we develop the theory of nonlinear rough paths. Following the ideas of Lyons and Gubinelli, we define the nonlinear rough integral ∫ts W(dr, Yr), where W and Y are only α-Hölder continuous in time with α ∈ (13,12]. Also, we study the Kunita-type equation Yt = ξ + ∫t0 W(dr, Ys), obtaining the local and global existence and uniqueness of the solution under suitable sufficient conditions. As an application, we study transport equations with rough vector fields and observe that the classical solution formula for smooth and Young’s cases does not provide a solution to the rough equation. Indeed this formula satisfies a transport equation with additional compensator terms (see (1.7)).

Item Type:	Article
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Instituto Nacional de Matemática Pura e Aplicada
ISSN:	1980-0436
Date of First Compliant Deposit:	2 September 2024
Date of Acceptance:	7 May 2020
Last Modified:	02 Oct 2024 01:30
URI:	https://orca.cardiff.ac.uk/id/eprint/171077

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