ICTP Mathematics Basic Notions Seminar - Thursday 11 February at 14:30

[Math Section]

B A S I C   N O T I O N S   S E M I N A R   S E R I E S   2016


Thursday, 11 February at 14:30


G.R. Moreno Flores (PUC, Chile)


Title: "A glimpse at rough integrals and rough differential equations"

Abstract:  Non-differentiable continuous functions appear in a variety 
of contexts. For example, the Black-Scholes equations from finance are 
differential equations driven by a Brownian motion, which itself is an 
example of a (random) non-differentiable continuous function. To solve 
these equations, we must be able to integrate against functions which 
are not even of bounded variation, so that Riemann-Stieljes integration 
cannot be used.

In this talk, we will give a brief overview of the theory of rough paths 
which extends the more familiar Riemann-Stieljes and Young integrals to 
very irregular functions, and allows to treat such differential 
equations. We will focus on the theory of controlled rough paths 
introduced by Gubinelli in 2004.

The talk should be accessible to students with a background in real 
analysis. No knowledge of probability is required.


VENUE:  Budinich Lecture Hall (ICTP Leonardo da Vinci Building)