By Prof. Simon Malham (Heriot-Watt University,UK)
The first part of my talk will be targeted towards a general mathematics audience. Hence we will start with an introduction to stochastic differential equations, how to interpret them, what information do we want to retrieve from them and how to retrieve it? I will discuss basic stochastic Taylor methods for strong simulation and the issues and difficulties that underlie higher order integrators.
In the second part of my talk we investigate the algebraic structure underlying the stochastic Taylor solution expansion for stochastic differential systems. Our motivation is to construct efficient integrators. These are approximations that generate strong numerical integration schemes that are more accurate than the corresponding stochastic Taylor approximation, independent of the governing vector fields and to all orders. The sinhlog integrator is one example.
We show that the natural context to study stochastic integrators and their properties is the convolution shuffle algebra of endomorphisms. We establish a new whole class of efficient integrators; and then prove that, within this class, the sinhlog integrator generates the optimal efficient stochastic integrator at all orders.
Biography: After finishing my PhD at Imperial in 1993, I spend three years at the University of Arizona. Then two years at Nottingham and two years at Imperial as a temporary lecturer followed. I joined Heriot-Watt in September 2000.
For more info contact: Prof. David Ketcheson : email: email@example.com
Date: Thursday 27th Apr 2017
Time:12:00 PM - 13:00 PM
Location: Building 9, Hall 1
Light Lunch will be available at 11:45 AM