# Zachary Selk (Queen's University)

Date

Wednesday February 8, 202312:00 pm - 1:00 pm

Location

Jeffery Hall, Room 319## Probability Seminar

**Wednesday, February 8th, 2023**

**Time:** 12:00 p.m. **Place:** Jeffery Hall, Room 319

**Speaker:** Zachary Selk (Queen's University)

**Title:** Trapezoid Rule for Rough Paths

**Abstract:** Rough paths theory is an alternative theory of solving stochastic differential equations to the classical Ito theory. Rough paths have two main advantages over Ito theory. First, it can be used to solve differential equations driven by more general processes than semi-martingales. Second, it can be used to solve differential equations in a pathwise way. Furthermore the solution map is continuous - that is, given two instances of driving signals that are close the solutions are also close.

The so-called "rough integral" is a standard Riemann-Stieltjes integral with an additional "correction term" which can be viewed as encoding a kind of "iterated integral" of the driving signal against itself. This correction term can be seen as unnatural. In this talk, we show for a wide class of Gaussian processes including the fractional Brownian motion one can simply use the trapezoid rule. Joint work with Yanghui Liu and Samy Tindel.