Construction of a Mean Square Error Adaptive Euler-Maruyama Method With Applications in Multilevel Monte Carlo

@inproceedings{Hoel2014ConstructionOA,
  title={Construction of a Mean Square Error Adaptive Euler-Maruyama Method With Applications in Multilevel Monte Carlo},
  author={H{\aa}kon Hoel and Juho H{\"a}pp{\"o}l{\"a} and R. Tempone},
  booktitle={MCQMC},
  year={2014}
}
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 pathwise a posteriori adaptive time stepping Euler--Maruyama method for numerical solutions of SDE, and the resulting method is incorporated into a multilevel Monte Carlo (MLMC) method for weak approximations of SDE. This gives an efficient MSE adaptive MLMC method for handling a number of low-regularity… Expand

References

SHOWING 1-10 OF 39 REFERENCES
Adaptive Weak Approximation of Stochastic Differential Equations
Multilevel Monte Carlo method with applications to stochastic partial differential equations
Optimal approximation of stochastic differential equations by adaptive step-size control
Implementation and analysis of an adaptive multilevel Monte Carlo algorithm
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