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Information × Registration Number 0121U111201, ( 0222U001234  ) R & D request Title Parameter estimation, hypothesis testing and forecasting in current stochastic models Head Mishura Yuliia S., Доктор фізико-математичних наук Registration Date 28-05-2021 Organization Taras Shevchenko National University of Kyiv popup.description1 Research of a wide class of stochastic models with both discrete and continuous time. It is planned to consider regression error models in the presence of censored observations and to extend the method of sufficient statistics to such models, which are very common in medical statistics. When assessing radiation risks from irradiation, the individual radiation dose is the result of complex processing of disparate individual data, resulting in a mixture of classical and Berkson errors. It is planned to develop a holistic theory for estimating risk factors in appropriate models with binary response and risk linear with respect to individual radiation dose. It is planned to consider the multidimensional problem of complete least squares with Vandermond structure and apply the method of correction of the penalty function, because in this case the known methods of estimating the transition matrix are unstable and have a significant systematic deviation from the true value. Stochastic models are constructed continuously as solutions of stochastic differential equations, and the wear and diffusion coefficients depend on the solutions, and the properties of the solutions and the estimation of the coefficients significantly depend on which random process is the driver. The project provides a wide range of related problems, including estimating unknown parameters for Cox-Ingersoll-Ross equations with a Wiener driver and a power diffusion coefficient, as well as with a fractional Brownian and more general Gaussian driver, and for Huesto models. In models with fractional Brownian motion, it is planned to develop comprehensive estimates for Hurst parameters and other model parameters. It is also planned to construct coefficient estimates for equations with subordinate processes. In addition, it is envisaged to apply the developed approaches to the study of processes considered in financial and actuarial mathematics, biology and physics. popup.nrat_date 2024-12-09 Close