Construction of geometric rough paths

Abstract:

 

This talk is based on a joint work in progress with L. Zambotti (UPMC). First, I will give a brief introduction to the theory of rough paths focusing on the case of Hölder regularity between 1/3 and 1/2. After this, I will address the basic problem of construction of a geometric rough path over a given ɑ-Hölder path in a finite-dimensional vector space. Although this problem was already solved by Lyons and Victoir in 2007, their method relies on the axiom of choice and thus is not explicit; in exchange the proof is simpler. In an upcoming paper, we provide an explicit construction clarifying the connection between rough paths theory and free (nilpotent) Lie algebras. In particular, we use an explicit form of the Baker–Campbell–Hausdorff formula due to Loday in order to provide explicit expressions and bounds to achieve such a construction.

Date: Nov 27, 2017 at 16:00 h
Venue: Beauchef 851, Torre Norte de Depto. de Ingeniería Matemática, 5to piso, Sala de Seminarios Felipe Álvarez Daziano.
Speaker: Nikolas Tapia
Affiliation: Universidad de Chile
Coordinator: Prof. Daniel Remenik
Abstract:
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Posted on Nov 21, 2017 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars