Webinar DISA-DSM November 10th
2020-11-06
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)
