Stabilized multilevel Monte Carlo method for stiff stochastic differential equations

DOI10.1016/j.jcp.2013.05.039zbMath1349.65028OpenAlexW2000136588MaRDI QIDQ347978

Adrian Blumenthal, Assyr Abdulle

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: http://infoscience.epfl.ch/record/183502

zbMATH Keywords

stabilitystochastic differential equationsstiffnessmultilevel Monte CarloS-ROCK method

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items

Optimal Explicit Stabilized Integrator of Weak Order 1 for Stiff and Ergodic Stochastic Differential Equations, A computational method for solving stochastic Itô-Volterra integral equations based on stochastic operational matrix for generalized hat basis functions, Algorithms for integration of stochastic differential equations using parallel optimized sampling in the Stratonovich calculus, Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions, Wavelets Galerkin method for solving stochastic heat equation, On multilevel Monte Carlo methods for deterministic and uncertain hyperbolic systems, Rapid Covariance-Based Sampling of Linear SPDE Approximations in the Multilevel Monte Carlo Method, Unnamed Item, Study of micro-macro acceleration schemes for linear slow-fast stochastic differential equations with additive noise, Wavelets method for solving nonlinear stochastic Itô-Volterra integral equations, New explicit stabilized stochastic Runge-Kutta methods with weak second order for stiff Itô stochastic differential equations, An efficient computational method for solving nonlinear stochastic Itô integral equations: application for stochastic problems in physics, Unnamed Item, Improved Stabilized Multilevel Monte Carlo Method for Stiff Stochastic Differential Equations

Uses Software

• RODAS
• PIROCK
• S-ROCK

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Simulation of human ischemic stroke in realistic 3D geometry
• PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise
• Mean-square stability of second-order Runge-Kutta methods for multi-dimensional linear stochastic differential systems
• Numerical solution of stochastic differential equations with jumps in finance
• S-ROCK methods for stiff Itô SDEs
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Monte Carlo complexity of global solution of integral equations
• Stochastic stabilization and destabilization
• Mean-square stability of numerical schemes for stochastic differential systems
• On roots and error constants of optimal stability polynomials
• Mathematical biology. Vol. 1: An introduction.
• Nonnormality and stochastic differential equations
• Stabilized methods for stiff stochastic systems
• Numerical techniques for multi-scale dynamical systems with stochastic effects
• Continuous Markov processes and stochastic equations
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• Fourth Order Chebyshev Methods with Recurrence Relation
• Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs
• Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations
• Towards a Systematic Linear Stability Analysis of Numerical Methods for Systems of Stochastic Differential Equations
• Multilevel Monte Carlo Path Simulation
• S-ROCK: Chebyshev Methods for Stiff Stochastic Differential Equations
• On the Internal Stability of Explicit,m-Stage Runge-Kutta Methods for Largem-Values
• Approximate travelling waves for generalized KPP equations and classical mechanics
• Stochastic Finite Differences and Multilevel Monte Carlo for a Class of SPDEs in Finance
• Multilevel Monte Carlo method with applications to stochastic partial differential equations
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations
• Multilevel Monte Carlo Methods for Stochastic Elliptic Multiscale PDEs
• Second order Chebyshev methods based on orthogonal polynomials