### Abstract

We study the problem of simulating the slow observable of a multiscale diffusion process. In particular, we extend previous algorithms to the case where the simulation of the different scales cannot be uncoupled and we have no explicit knowledge of the drift or the variance of the multiscale diffusion. This is the case when the simulation data come from a black box "legacy code," or possibly from a fine scale simulator (e.g., MD, kMC) which we want to effectively model as a diffusion process. We improve the algorithm, using the past simulations as control variates, in order to reduce the variance of the subsequent simulations.

Original language | English (US) |
---|---|

Pages (from-to) | 70-89 |

Number of pages | 20 |

Journal | Multiscale Modeling and Simulation |

Volume | 6 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 2007 |

### All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Modeling and Simulation
- Ecological Modeling
- Physics and Astronomy(all)
- Computer Science Applications

### Keywords

- Control variates
- Equation-free
- Projective integration
- Stochastic multiscale methods
- Variance reduction

## Fingerprint Dive into the research topics of 'Variance reduction for the equation-free simulation of multiscale stochastic systems'. Together they form a unique fingerprint.

## Cite this

Papavasiliou, A., & Kevrekidis, Y. (2007). Variance reduction for the equation-free simulation of multiscale stochastic systems.

*Multiscale Modeling and Simulation*,*6*(1), 70-89. https://doi.org/10.1137/060650635