86 citations · 109 across the 10 of their papers we have counts for
13 papers
The multi-index Monte Carlo method for semilinear stochastic partial differential equations
Abdul-Lateef Haji-Ali, Håkon Hoel, Andreas Petersson
Stochastic partial differential equations (SPDEs) are often difficult to solve numerically due to their low regularity and high dimensionality. These challenges limit the practical…
A Fast and Accurate Numerical Method for the Left Tail of Sums of Independent Random Variables
Nadhir Ben Rached, Håkon Hoel, Johannes Vincent Meo
We present a flexible, deterministic numerical method for computing left-tail rare events of sums of non-negative, independent random variables. The method is based on iterative nu…
Higher-order adaptive methods for exit times of Itô diffusions
Håkon Hoel, Sankarasubramanian Ragunathan
We construct a higher-order adaptive method for strong approximations of exit times of Itô stochastic differential equations (SDE). The method employs a strong Itô--Taylor scheme f…
Improved Efficiency of Multilevel Monte Carlo for Stochastic PDE through Strong Pairwise Coupling
Neil K. Chada, Håkon Hoel, Ajay Jasra +1
Multilevel Monte Carlo (MLMC) has become an important methodology in applied mathematics for reducing the computational cost of weak approximations. For many problems, it is well-k…
Multi-index ensemble Kalman filtering
Håkon Hoel, Gaukhar Shaimerdenova, Raúl Tempone
In this work we combine ideas from multi-index Monte Carlo and ensemble Kalman filtering (EnKF) to produce a highly efficient filtering method called multi-index EnKF (MIEnKF). MIE…
Weak convergence analysis in the particle limit of the McKean--Vlasov equations using stochastic flows of particle systems
Abdul-Lateef Haji-Ali, Håkon Hoel, Raúl Tempone
We present a proof showing that the weak error of a system of interacting stochastic particles approximating the solution of the McKean-Vlasov equation is .…
Central limit theorems for multilevel Monte Carlo methods
Håkon Hoel, Sebastian Krumscheid
In this work, we show that uniform integrability is not a necessary condition for central limit theorems (CLT) to hold for normalized multilevel Monte Carlo (MLMC) estimators and w…
Multilevel ensemble Kalman filtering for spatio-temporal processes
Alexey Chernov, Håkon Hoel, Kody J. H. Law +2
We design and analyse the performance of a multilevel ensemble Kalman filter method (MLEnKF) for filtering settings where the underlying state-space model is an infinite-dimensiona…
Computable error estimates for finite element approximations of elliptic partial differential equations with rough stochastic data
Eric Joseph Hall, Håkon Hoel, Mattias Sandberg +2
We derive computable error estimates for finite element approximations of linear elliptic partial differential equations (PDE) with rough stochastic coefficients. In this setting,…
Multilevel ensemble Kalman filtering
Håkon Hoel, Kody J. H. Law, Raul Tempone
This work embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and…
Construction of a Mean Square Error Adaptive Euler--Maruyama Method with Applications in Multilevel Monte Carlo
Håkon Hoel, Juho Häppölä, Raúl Tempone
A formal mean square error expansion (MSE) is derived for Euler--Maruyama numerical solutions of stochastic differential equations (SDE). The error expansion is used to construct a…
Computational error estimates for Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces
Christian Bayer, Hakon Hoel, Ashraful Kadir +3
The difference of the values of observables for the time-independent Schroedinger equation, with matrix valued potentials, and the values of observables for ab initio Born-Oppenhei…
How accurate is molecular dynamics?
Christian Bayer, Håkon Hoel, Petr Plecháč +2
Born-Oppenheimer dynamics is shown to provide an accurate approximation of time-independent Schrödinger observables for a molecular system with an electron spectral gap, in the lim…