Semi-Parametric Drift and Diffusion Estimation for Multiscale Diffusions

Abstract

We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective equation describing the dynamics on the longer diffusive time scale, i.e. in a homogenization framework. We examine the case where both the drift and the diffusion coefficients in the effective dynamics are space-dependent and depend on multiple unknown parameters. It is known that classical estimators, such as Maximum Likelihood and Quadratic Variation of the Path Estimators, fail to obtain reasonable estimates for parameters in the effective dynamics when based on observations of the underlying multiscale diffusion. We propose a novel algorithm for estimating both the drift and diffusion coefficients in the effective dynamics based on a semi-parametric framework. We demonstrate by means of extensive numerical simulations of a number of selected examples that the algorithm performs well when applied to data from a multiscale diffusion. These examples also illustrate that the algorithm can be used effectively to obtain accurate and unbiased estimates.

32 pages, 10 figures

References in corpus (6)

• Parameter Estimation for Multiscale Diffusions
• Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations
• A Note on Diffusion Limits of Chaotic Skew Product Flows
• Noise induced state transitions, intermittency and universality in the noisy Kuramoto-Sivashinsky equation
• Numerical methods for stochastic partial differential equations with multiples scales
• Additive noise effects in active nonlinear spatially extended systems

Cited by in corpus (2)

• State and Parameter Estimation from Observed Signal Increments
• Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering