Stochastic stabilization and destabilization
Systems & Control Letters
Stability Analysis of Numerical Schemes for Stochastic Differential Equations
SIAM Journal on Numerical Analysis
Monte Carlo complexity of global solution of integral equations
Journal of Complexity
Fourth Order Chebyshev Methods with Recurrence Relation
SIAM Journal on Scientific Computing
S-ROCK: Chebyshev Methods for Stiff Stochastic Differential Equations
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Multilevel Monte Carlo Path Simulation
Operations Research
SIAM Journal on Numerical Analysis
Multilevel Monte Carlo method with applications to stochastic partial differential equations
International Journal of Computer Mathematics - RECENT ADVANCES ON THE NUMERICAL SOLUTIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
Hi-index | 31.45 |
A multilevel Monte Carlo (MLMC) method for mean square stable stochastic differential equations with multiple scales is proposed. For such problems, that we call stiff, the performance of MLMC methods based on classical explicit methods deteriorates because of the time step restriction to resolve the fastest scales that prevents to exploit all the levels of the MLMC approach. We show that by switching to explicit stabilized stochastic methods and balancing the stabilization procedure simultaneously with the hierarchical sampling strategy of MLMC methods, the computational cost for stiff systems is significantly reduced, while keeping the computational algorithm fully explicit and easy to implement. Numerical experiments on linear and nonlinear stochastic differential equations and on a stochastic partial differential equation illustrate the performance of the stabilized MLMC method and corroborate our theoretical findings.