# Martingale product estimators for sensitivity analysis in computational statistical physics

@article{Plech2021MartingalePE, title={Martingale product estimators for sensitivity analysis in computational statistical physics}, author={Petr Plech{\'a}{\vc} and Gabriel Stoltz and Ting Wang}, journal={ArXiv}, year={2021}, volume={abs/2112.00126} }

We introduce a new class of estimators for the linear response of steady states of stochastic dynamics. We generalize the likelihood ratio approach and formulate the linear response as a product of two martingales, hence the name ”martingale product estimators”. We present a systematic derivation of the martingale product estimator, and show how to construct such estimator so its bias is consistent with the weak order of the numerical scheme that approximates the underlying stochastic…

## 2 Citations

### Error estimates and variance reduction for nonequilibrium stochastic dynamics

- PhysicsArXiv
- 2022

Equilibrium properties in statistical physics are obtained by computing averages with respect to Boltzmann–Gibbs measures, sampled in practice using ergodic dynamics such as the Langevin dynamics.…

### Mobility estimation for Langevin dynamics using control variates

- MathematicsArXiv
- 2022

The scaling of the mobility of two-dimensional Langevin dynamics in a periodic potential as the friction vanishes is not well understood for non-separable potentials. Theoretical results are lacking,…

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