Statistical inference for rough volatility: Minimax theory Page 1 The Annals of Statistics 2024,
Vol. 52, No. 4, 1277–1306 https://doi.org/10.1214/23-AOS2343 © Institute of Mathematical …

In recent years, there has been a substantive interest in rough volatility models. In this class
of models, the local behavior of stochastic volatility is much more irregular than …

We develop a nonparametric test for deciding whether volatility of an asset follows a
standard semimartingale process, with paths of finite quadratic variation, or a rough process …

The analysis and detection of sleep stages continue to preoccupy researchers, particularly
bioinformaticians and neurologists aiming to understand various aspects and functioning of …

The online supplement [18] to this article contains the formal proofs of the results. Section A
of this supplement recalls important notation, Section B gives necessary technical results …

Some problems in the theory and applications of stochastic processes can be reduced to
solving integral equations. Such equations, however, rarely have explicit solutions. Useful …

This paper addresses the problem of estimating the Hurst exponent of the fractional
Brownian motion from continuous time noisy sample. When the Hurst parameter is greater …

In recent years, there has been substantive empirical evidence that stochastic volatility is
rough. In other words, the local behavior of stochastic volatility is much more irregular than …

We investigate the Local Asymptotic Property for fractional Brownian models based on
discrete observations contaminated by a Gaussian moving average process. We consider …

In this article, we consider the problem of estimating fractional processes based on noisy
high-frequency data. Generalizing the idea of pre-averaging to a fractional setting, we …