My research

In my current postdoc I am interested in understanding and quantifying feedbacks between diurnal warm layers in the tropical Atlantic ocean and shallow convection. For this I mainly use the output of ICON simulations, but also observational data.

In mathematics, my research interests lie in stochastic (partial) differential equations driven by fractional Brownian motion (or other Hermite processes) and applications in statistical inference. I am also interested in studying random fields on the sphere. In the majority of my works I use the Malliavin-Stein machinery for Gaussian processes, and I am fascinated by its various applications.

At the intersection of mathematics and earth sciences my interests are in demonstrating theoretical results for equations in oceanography having a random component.

At present, all publications and preprints listed below contain only my work in mathematics. Note that the authors in such papers are listed alphabetically.

Publications

J. Gairing, P. Imkeller, R. Shevchenko, C. A. Tudor – Hurst index estimation in stochastic differential equations driven by fractional Brownian motion.
Journal of Theoretical Probability, 33, 1691-1714 (2019).
R. Shevchenko, M. Slaoui, C. A. Tudor – Generalised k-variations and Hurst parameter estimation for the fractional wave equation via Malliavin calculus.
Journal of Statistical Planning anf Inference, 207, 155-180 (2020).
R. Shevchenko, C. A. Tudor – Parameter estimation for the Rosenblatt Ornstein-Uhlenbeck process with periodic mean.
Statistical Inference for Stochastic Processes, 23, 227-247 (2020).
R. Shevchenko, J. H. C. Woerner – Inference for fractional Ornstein-Uhlenbeck type processes with periodic mean in the non-ergodic case.
Stochastic Analysis and Applications (2021).

Preprints

R. Shevchenko, A. P. Todino – Asymptotic behaviour of level sets of needlet random fields.
Preprint, submitted. arXiv:2011.02856 (2020).
R. Shevchenko – Quadratic variations for Gaussian isotropic random fields on the sphere.
Preprint, submitted. arXiv:2105.11970 (2021).
R. Shevchenko – On quadratic variations for the fractional-white wave equation. Preprint, submitted (2021).

Other materials

R. Shevchenko – Limit theorems and statistical inference for solutions of some stochastic (partial) differential equations.
PhD Thesis, Technische Universitat Dortmund (2020).