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SUMMARY:Statistical Inference for the Rough Homogenization Limit of Multis
 cale Fractional Ornstein-Uhlenbeck Processes - Pablo Ramses Alonso Martin 
 (University of Warwick)
DTSTART:20240904T104500Z
DTEND:20240904T110500Z
UID:TALK219127@talks.cam.ac.uk
DESCRIPTION:Most real-world systems exhibit a multiscale behaviour that ne
 eds to be taken into consideration when fitting the effective dynamics to 
 data sampled at a given scale. In the case of stochastic multiscale system
 s driven by Brownian motion\, it has been shown that in order for the Maxi
 mum Likelihood Estimators of the parameters of the limiting dynamics to be
  consistent\, data needs to be subsampled at an appropriate rate. Recent a
 dvances in extracting effective dynamics for fractional multiscale systems
  make the same question relevant in the fractional diffusion setting. We s
 tudy the problem of parameter estimation of the diffusion coefficient in t
 his context. In particular\, we consider the multiscale fractional Ornstei
 n-Uhlenbeck system (fractional kinetic Brownian motion) and we provide con
 vergence results for the &nbsp\;Maximum Likelihood Estimator of the diffus
 ion coefficient of the limiting dynamics\, using multiscale data. To do so
 \, we derive asymptotic bounds for the spectral norm of the inverse covari
 ance matrix of fractional Gaussian noise. This is joint work with Anastasi
 a Papavasiliou and Horatio Boedihardjo.
LOCATION:Seminar Room 1\, Newton Institute
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