Volterra Rough Equations

Xiaohua Wang, Purdue University

Abstract

This article is devoted to extend the recently developed rough path theory for Volterra equations from [1] to the case of more rough noise and/or more singular Volterra kernels. It was already observed in [1] that the Volterra rough path introduced there did not satisfy any geometric relation, similar to that observed in classical rough path theory. Thus, an extension of the theory to more irregular driving signals requires a deeper understanding of the specific algebraic structure arising in the Volterra rough path. Inspired by the elements of ”non-geometric rough paths” developed in [2] and [3] tree rooted index is a simple description of the Volterra rough path and the controlled Volterra process, and with this description the existence and uniqueness of the solution to rough volterra equations driven by more irregular signals are held.

Degree

Ph.D.

Advisors

Tindel, Purdue University.

Subject Area

Mathematics|Systems science

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