Search academic texts

Information × Registration Number 0221U101135, 0120U105320 , R & D reports Title Parameter estimation, hypothesis testing and forecasting in current stochastic models. popup.stage_title Head Mishura Yuliia S., Доктор фізико-математичних наук Registration Date 15-01-2021 Organization Taras Shevchenko National University of Kyiv popup.description2 The object of study - random processes, stochastic differential equations, diffusion models with stochastic volatility, regression models. The aim of the work is to study statistical problems for a wide class of stochastic models with both discrete and continuous time and their application in financial and actuarial mathematics, biology and physics. Research methods - analytical methods of probability theory and mathematical statistics, methods of stochastic analysis, theory of random processes, functional analysis, theory of partial differential equations, fractional analysis, computer modeling of random processes. The main research results obtained in the work: The model of linear regression in the presence of a mixture of classical and Berkson error in the regressor is considered. In this model, strictly consistent estimates of all unknown parameters of the model are constructed and their asymptotic normality is proved. The model is modified to distinguish two groups of asymptotically independent estimates, which allows us to construct an asymptotic confidence domain for the true values ​​of the parameters as the Cartesian product of two ellipsoids. The problem of estimating a low-rank complex Vandermond matrix by observing a perturbed matrix is ​​studied, and the additive noise is also with the Vandermond matrix, which is generated by independent Gaussian quantities with the same variances. Cases of both known and unknown noise dispersion are considered. The estimation of the structural vector defining the low-ranking Vandermond matrix is ​​constructed by the method of the corrected estimation function with the subsequent correction. The behavior of the proposed estimates depending on the number of rows per column in the Vandermond matrix was studied using numerical simulation. as well as from the noise dispersion. A continuous linear stochastic model with two noises, which are modeled by the Wiener process and fractional Brownian motion, is studied.   Product Description popup.authors Kukush Olexander G. Logvinenko Stanislav S. Ralchenko Kostiantyn V. Chernova Oksana O. Shkliar Sergiy V. popup.nrat_date 2021-01-15 Close