Fast and Accurate Simulation of Stochastic Differential Equations

Russel Caflisch
Institute for Pure and Applied Mathematics
Director

Numerical solution of stochastic differential equations (SDEs) is challenging because of the rapid fluctuations in white noise forcing. After a brief introduction to SDEs and their numerical simulation, the focus will be on the Milstein method that provides more accurate solutions to SDEs. In particular we present a method for efficient simulation of the Levy areas that occur in of Milstein for vector systems. Use of these results in multi-level Monte Carlo (MLMC) for vector systems will be discussed. Applications from finance and plasma physics will be presented. This work is in collaboration with Bruce Cohen and Andris Dimits (LLLNL) and with Lee Ricketson and Mark Rosin (UCLA).


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