Stochastic partial differential equations (SPDEs) are used in many areas of applied science and engineering. Examples of systems that are modeled by SPDEs arise in applications as diverse as satellite guidance, tumor detection and financial markets. In many instances analytic solutions to these equations are unavailable and approximations with a high order of accuracy are difficult to obtain.
We will recall an extrapolation technique known as Richardson's method and consider finite difference approximations for an important class of SPDEs arising in the nonlinear filtering theory. Then we will give sufficient conditions under which the strong rate of convergence with respect to the spatial approximation can be accelerated to an arbitrarily high order by Richardson's method.
A native of Philadelphia, Eric Hall earned his Bachelor Degree in mathematics at the University of Pennsylvania in 2008. He then joined the School of Mathematics at the University of Edinburgh in Edinburgh, United Kingdom as a graduate student. A member of the Probability and Stochastic Analysis research group, Eric received his Ph.D. in 2013 for research concerning accelerated numerical schemes for stochastic partial differential equations (SPDEs). Presently Eric is the Göran Gustafsson Postdoctoral Fellow in Mathematics at KTH Royal Institute of Technology in Stockholm, Sweden where he is a member of Numerical Analysis group.
His interests include numerical analysis, (S)PDEs and probability. More specifically, he is interested in higher order numerical approximations for SPDEs arising in the nonlinear filtering theory and, more recently, in numerical methods for PDEs with random coefficients.