We introduce a simulation scheme for Brownian semistationary processes, which is based
on discretizing the stochastic integral representation of the process in the time domain. We …

This paper proposes to model and forecast realized volatility (RV) using the fractional
Ornstein–Uhlenbeck (fO–U) process with a general Hurst parameter, H. A two-stage method …

This paper studies the least squares estimator (LSE) for the drift parameter of an Ornstein–
Uhlenbeck process driven by fractional Brownian motion, whose observations can be made …

Ambit stochastics is the name for the theory and applications of ambit fields and ambit
processes and constitutes a new research area in stochastics for tempo-spatial phenomena …

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 …

Ambit Stochastics has emerged as a new field in probability theory during the last decade.
While there are still many open questions and challenges, we think that the time is right to …

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 …

Supplement to “High-frequency analysis of parabolic stochastic PDEs”. This paper is
accompanied by supplementary material in [14]. Section A in [14] gives some auxiliary …

By reducing fossil fuel use, renewable energy improves the economy, quality of life, and
environment. These impacts make renewable energy forecasting crucial for lowering fossil …

In this paper we propose a new modelling framework for electricity futures markets based on
so-called ambit fields. The new model can capture many of the stylised facts observed in …