Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
Time: 16:30–18:30
Speaker 1: Long Ngo Hoang (Laboratory of Applied Mathematics)
Title: Well-posedness, regularity of solutions and the $\theta$-Euler-Maruyama scheme for stochastic Volterra integral equations with general singular kernels and jumps
Abstract:
In this talk, we consider a class of stochastic Volterra integral equations with general singular kernels, driven by a Brownian motion and a pure jump L\’evy process. We first show that these equations have a unique strong solution under certain regular conditions on their coefficients. Furthermore, the solutions of this equation depend continuously on the initial value and on the kernels $k$, $k_B$, and $k_Z$. We will then show the regularity of solutions for these equations. Finally, we propose a $\theta$-Euler-Maruyama approximation scheme for these equations and demonstrate its convergence at a certain rate in the $L^2$-norm.
This is a joint work with PHAN Thi Huong (Le Quy Don Technique University) and Peter Kloeden (Universit\”{a}t T\”{u}bingen)
Speaker 2: Tran Ngoc Khue (Hanoi University of Science and Technology)
Title:On the infinite time horizon approximation for Lévy-driven McKean-Vlasov SDEs with non-globally Lipschitz continuous and super-linearly growth drift and diffusion coefficients
Abstract:
This talk presents the study of the numerical approximation for McKean-Vlasov stochastic differential equations driven by Lévy processes. We propose a tamed-adaptive Euler-Maruyama scheme and consider its strong convergence in both finite and infinite time horizons when applying for some classes of Lévy-driven McKean-Vlasov stochastic differential equations with non-globally Lipschitz continuous and super-linearly growth drift and diffusion coefficients. This is a joint work with Hoang-Long Ngo, Duc-Trong Luong and Trung-Thuy Kieu.
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