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Statistical inference for perturbed multiscale dynamical systems

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  • Gailus, Siragan
  • Spiliopoulos, Konstantinos

Abstract

We study statistical inference for small-noise-perturbed multiscale dynamical systems. We prove consistency, asymptotic normality, and convergence of all scaled moments of an appropriately constructed maximum likelihood estimator (MLE) for a parameter of interest, identifying precisely its limiting variance. We allow full dependence of coefficients on both slow and fast processes, which take values in the full Euclidean space; coefficients in the equation for the slow process need not be bounded and there is no assumption of periodic dependence. The results provide a theoretical basis for calibration of small-noise-perturbed multiscale dynamical systems. Data from numerical simulations are presented to illustrate the theory.

Suggested Citation

  • Gailus, Siragan & Spiliopoulos, Konstantinos, 2017. "Statistical inference for perturbed multiscale dynamical systems," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 419-448.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:2:p:419-448
    DOI: 10.1016/j.spa.2016.06.013
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    References listed on IDEAS

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    1. Jin Feng & Jean-Pierre Fouque & Rohini Kumar, 2010. "Small-time asymptotics for fast mean-reverting stochastic volatility models," Papers 1009.2782, arXiv.org, revised Aug 2012.
    2. Veretennikov, A. Yu., 1997. "On polynomial mixing bounds for stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 115-127, October.
    3. Papavasiliou, A. & Pavliotis, G.A. & Stuart, A.M., 2009. "Maximum likelihood drift estimation for multiscale diffusions," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3173-3210, October.
    4. Konstantinos Spiliopoulos & Alexandra Chronopoulou, 2013. "Maximum likelihood estimation for small noise multiscale diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 16(3), pages 237-266, October.
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