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Seminar 2018

 
27 February 2018

Title : Why spectral methods are preferred in PDE eigenvalue computations in some cases?

Professor Zhimin Zhang

Time : 3.30pm – 4.30pm
Venue : MAS Executive Classroom 1 #03-06,
School of Physical and Mathematical Sciences

Abstract:
When approximating PDE eigenvalue problems by numerical methods such as finite difference and finite element, it is common knowledge that only a small portion of numerical eigenvalues are reliable. As a comparison, spectral methods may perform extremely well in some situation, especially for 1-D problems. In addition, we demonstrate that spectral methods can outperform traditional methods and the state-of-the-art method in 2-D problems even with singularities.

Host: Associate Professor Wang Li-Lian
Division of Mathematical Sciences, School of Physical and Mathematical Sciences

16 January 2018

Title : Limit theorems for the realised covariation of a bivariate Brownian semistationary process

Dr Andrea Granelli

Time : 11.00am – 12.00pm
Venue : MAS Executive Classroom 1 #03-06,
School of Physical and Mathematical Sciences

Abstract:
Within the realm of stochastic processes that fail to be a semimartingale, the recent literature has devoted particular attention to the Brownian semistationary process, a process that has originally been used in the context of turbulence modelling, but has subsequently been employed as a price process in energy markets.
This talk presents a weak law of large numbers and a central limit theorem for the scaled realised covariation of a bivariate Brownian semistationary process. The novelty of the results lies in the fact that we derive the suitable asymptotic theory both in a multivariate setting and outside the classical semimartingale framework. The proofs rely heavily on recent developments in Malliavin calculus.
This talk is based on joint work with Dr. Almut Veraart, reader in Statistics at Imperial College London.

Host: Dr Pun Chi Seng Patrick
Division of Mathematical Sciences, School of Physical and Mathematical Sciences