WIAS Preprint No. 381, (1997)

On estimating a dynamic function of stochastic system with averaging


  • Liptser, Robert
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62G05 62M99


  • fast and slow components, drift and diffusion coefficients, ergodic property, nonparametric estimation, bandwidth selection


We consider a two-scaled diffusion system, when drift and diffusion parameters of a "slow" component are contaminated by an unobservable "fast" one. The goal is to estimate the dynamic function which is defined by averaging the drift coefficient of the "slow" component w.r.t. the stationary distribution of the "fast" one. For estimation we use a locally linear smoother with a data-driven choice of bandwidth. A procedure proposed is fully adaptive and nearly optimal up to a log log factor.

Appeared in

  • Stat. Inference Stoch. Process., 3, no. 3 (2000),pp. 225 - 249.

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