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Generalizations of the Ornstein–Uhlenbeck process defined through Langevin equations, such as fractional Ornstein–Uhlenbeck processes, have recently received a lot of attention. However, most of the literature focuses on the one‐dimensional case with Gaussian noise. In particular, estimation of the unknown parameter is widely studied under Gaussian stationary increment noise. In this article, we consider estimation of the unknown model parameter in the multidimensional version of the Langevin equation, where the parameter is a matrix and the noise is a general, not necessarily Gaussian, vector‐valued process with stationary increments. Based on algebraic Riccati equations, we construct an estimator for the parameter matrix. Moreover, we prove the consistency of the estimator and derive its limiting distribution under natural assumptions. In addition, to motivate our work, we prove that the Langevin equation characterizes essentially all multidimensional stationary processes. [ABSTRACT FROM AUTHOR]

Seriously ill patients infected with severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2) and hospitalized in intensive care units (ICUs) are commonly given a combination of drugs, a process known as multi‐drug treatment. After extracting data on drug–drug interactions with clinical relevance from available online platforms, we hypothesize that an overall interaction map can be generated for all drugs administered. Furthermore, by combining this approach with simulations of cellular biochemical pathways, we may be able to explain the general clinical outcome. Finally, we postulate that by applying this strategy retrospectively to a cohort of patients hospitalized in ICU, a prediction of the timing of developing acute kidney injury (AKI) could be made. Whether or not this approach can be extended to other diseases is uncertain. Still, we believe it represents a valuable pharmacological insight to help improve clinical outcomes for severely ill patients. [ABSTRACT FROM AUTHOR]

ABSTRACT We study the asymptotic behaviour of the maximum likelihood estimator corresponding to the observation of a trajectory of a skew Brownian motion, through a uniform time discretization. We characterize the speed of convergence and the limiting distribution when the step size goes to zero, which in this case are non-classical, under the null hypothesis of the skew Brownian motion being an usual Brownian motion. This allows to design a test on the skewness parameter. We show that numerical simulations can be easily performed to estimate the skewness parameter and provide an application in Biology. [ABSTRACT FROM AUTHOR]