DISA

The DISA-DSM group welcomes you to a webinar with Yaozhong Hu   (University Alberta, Edmonton, Canada) 10 November at 13:00 Stockholm time

Title: Numerical methods for stochastic Volterra integral equations with weakly singular kernels

Abstract: In this talk, we  will introduce  stochastic Volterra integral equations with weakly singular kernels and study the existence, uniqueness and Holder continuity of the solution. Then, we propose a  theta-Euler-Maruyama  scheme  and a Milstein scheme to solve  the equations numerically  and  we obtain the strong  rates of convergence for both schemes in L^{p} norm for any p\geq 1. For the theta-Euler-Maruyama  scheme the rate is min {1-alpha, 1\2-beta} and for the Milstein scheme the rate is min{1-alpha,1-2beta} when alpha\neq \frac 12, where 0<alpha<1, 0< beta<1\2. These  results on the rates of convergence are significantly different from that of the similar schemes for the stochastic Volterra integral equations with regular  kernels. The difficulty to obtain our results is the lack of Ito formula for the equations. To get around of this difficulty we use instead the Taylor formula and then carry a sophisticated  analysis on the equation the solution satisfies.

For more information and registration contact Nacira Agram – nacira.agram@lnu.se

Upcoming seminars:

• 17 November  at 13:00 – Paolo Di Tella (University of Technology Dresden, Germany) Title: On enlarged filtrations of point processes
• 24 November  at 12:00 – David SISKA (University of Edinburg, UK)
• 24 November  at 13:00 WEINAN E  (Princeton University, USA) Title: An Overview of Deep Learning Based Algorithms for high dimensional PDEs Abstract: I will give an overview of deep learning-based algorithms for PDEs. Topics to be covered includes: (1) The Deep BSDE method. (2) Applications to control theory. (3) Theoretical advances.
• 30 November at 15:00 Jiequn Han (Princeton University, USA)
•  8 December at 13:00 Stockholm time Mathieu Lauriere (Princeton University, USA)