Open Access
April 2020 High-frequency analysis of parabolic stochastic PDEs
Carsten Chong
Ann. Statist. 48(2): 1143-1167 (April 2020). DOI: 10.1214/19-AOS1841


We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at high temporal frequency, we use limit theorems for multipower variations and related functionals to construct consistent nonparametric estimators and asymptotic confidence bounds for the integrated volatility process. As a byproduct of our analysis, we also obtain feasible estimators for the regularity of the spatial covariance function of the noise.


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Carsten Chong. "High-frequency analysis of parabolic stochastic PDEs." Ann. Statist. 48 (2) 1143 - 1167, April 2020.


Received: 1 June 2018; Revised: 1 March 2019; Published: April 2020
First available in Project Euclid: 26 May 2020

zbMATH: 07241584
MathSciNet: MR4102691
Digital Object Identifier: 10.1214/19-AOS1841

Primary: 60H15 , 62G20 , 62M40

Keywords: high-frequency observations , martingale limit theorems , multipower variations , SPDEs , Stochastic heat equation , variation functionals , Volatility estimation

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 2 • April 2020
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