85 citations · 207 across the 20 of their papers we have counts for
15 papers · 1 filter
An Adaptive Sampling Algorithm for Level-set Approximation
Matteo Croci, Abdul-Lateef Haji-Ali, Ian C. J. Powell
We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive…
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…
Forward Propagation of Low Discrepancy Through McKean-Vlasov Dynamics: From QMC to MLQMC
Nadhir Ben Rached, Abdul-Lateef Haji-Ali, Raúl Tempone +1
This work develops a particle system addressing the approximation of McKean-Vlasov stochastic differential equations (SDEs). The novelty of the approach lies in involving low discr…
Multi-index importance sampling for McKean--Vlasov stochastic differential equations
Nadhir Ben Rached, Abdul-Lateef Haji-Ali, Shyam Mohan Subbiah Pillai +1
This work addresses the estimation of rare-event quantities expressed as expectations of smooth observables of solutions to a broad class of McKean--Vlasov stochastic differential…
Multilevel Path Branching for Digital Options
Michael B. Giles, Abdul-Lateef Haji-Ali
We propose a new Monte Carlo-based estimator for digital options with assets modelled by a stochastic differential equation (SDE). The new estimator is based on repeated path split…
Multilevel Importance Sampling for Rare Events Associated With the McKean--Vlasov Equation
Nadhir Ben Rached, Abdul-Lateef Haji-Ali, Shyam Mohan Subbiah Pillai +1
This work combines multilevel Monte Carlo (MLMC) with importance sampling to estimate rare-event quantities that can be expressed as the expectation of a Lipschitz observable of th…
Double-Loop Importance Sampling for McKean--Vlasov Stochastic Differential Equation
Nadhir Ben Rached, Abdul-Lateef Haji-Ali, Shyam Mohan Subbiah Pillai +1
This paper investigates Monte Carlo (MC) methods to estimate probabilities of rare events associated with solutions to the -dimensional McKean-Vlasov stochastic differential equ…
Multilevel weighted least squares polynomial approximation
Abdul-Lateef Haji-Ali, Fabio Nobile, Raúl Tempone +1
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distr…
Multilevel and Multi-index Monte Carlo methods for the McKean-Vlasov equation
Abdul-Lateef Haji-Ali, Raul Tempone
We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of pa…
Multi-index Stochastic Collocation convergence rates for random PDEs with parametric regularity
Abdul-Lateef Haji-Ali, Fabio Nobile, Lorenzo Tamellini +1
We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDEs) with random data, where th…
Novel results for the anisotropic sparse grid quadrature
Abdul-Lateef Haji-Ali, Helmut Harbrecht, Michael Peters +1
This article is dedicated to the anisotropic sparse grid quadrature for functions which are analytically extendable into an anisotropic tensor product domain. Taking into account t…
Multi-Index Stochastic Collocation for random PDEs
Abdul-Lateef Haji-Ali, Fabio Nobile, Lorenzo Tamellini +1
In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique b…
Multi-Index Monte Carlo: When Sparsity Meets Sampling
Abdul-Lateef Haji-Ali, Fabio Nobile, Raul Tempone
We propose and analyze a novel Multi-Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven…
Optimization of mesh hierarchies in Multilevel Monte Carlo samplers
Abdul Lateef Haji Ali, Fabio Nobile, Erik von Schwerin +1
We perform a general optimization of the parameters in the Multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation…
A Continuation Multilevel Monte Carlo algorithm
Nathan Collier, Abdul-Lateef Haji-Ali, Fabio Nobile +2
We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem fo…