Publications (4)
Analysis of circulant embedding methods for sampling stationary random fields
Ivan G. Graham, Frances Y. Kuo, Dirk Nuyens +2
In this paper we prove, under mild conditions, that the positive definiteness of the circulant matrix appearing in the circulant embedding method is always guaranteed, provided the…
Improving MLMC for SDEs with application to the Langevin equation
Eike H. Mueller, Rob Scheichl, Tony Shardlow
This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the Multilevel Monte Carlo (MLMC) met…
Circulant embedding with QMC -- analysis for elliptic PDE with lognormal coefficients
Ivan G. Graham, Frances Y. Kuo, Dirk Nuyens +2
In a previous paper (J. Comp. Phys. 230 (2011), 3668--3694), the authors proposed a new practical method for computing expected values of functionals of solutions for certain class…
Continuous Level Monte Carlo and Sample-Adaptive Model Hierarchies
Gianluca Detommaso, Tim Dodwell, Rob Scheichl
In this paper, we present a generalisation of the Multilevel Monte Carlo (MLMC) method to a setting where the level parameter is a continuous variable. This Continuous Level Monte…