Registration Number
0224U031596,
0122U001843
, R & D reports
Title
Stochastic dynamical systems, inhomogeneous in time or random time: asymptotics and statistical analysis
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Head
Mishura Yuliia S., Доктор фізико-математичних наук
Registration Date
21-05-2024
Organization
Taras Shevchenko National University of Kyiv
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The goodness-of-fit test in the implicit regression model with measurement errors was studied. In the model of estimation of parameters of two straight lines by perturbed observations of points on the selines, the asymptotic distribution of the goodness-of-fit test statistics is obtained. Polynomial recurrence for inhomogeneous Markov chains is established, which plays a key role in the construction of coupling for a pair of different time-inhomogeneous chains. The Foster-Lyapunov condition known in the theory of homogeneous Markov chains, which guarantees polynomial recurrence, is generalized to the case of inhomogeneous Markov chains. The obtained estimates are applied to inhomogeneous random walkon a half-line. Sufficient conditions are found for a one-dimensional Lévy-type process under which theprocess (provided that it exists) will be reversible or irreversible and ergodic. The asymptotic behavior of the potential corresponding to the risk process with incomes, which is a Markov process of a certain type, isestablished. The sample paths properties of stochastic processes representing the solutions to partial differential equations with random initial conditions have been studied, the estimates for the distributions of suprema on bounded domains and the rate of growth on unbounded domains under different conditions on the increments of processes are stated. Generalized counting processes with random time-changebymeans of subordinators and inverse subordinators were studied. Formulas for distributions and equations for distributions and generating functions in terms of differential-convolution operators are established. The necessary and sufficient conditions for the existence of a stationary solution to the planar autoregressive first order model are obtained, as well as the conditions for causality of the solution. The explicit formulas for the asymptotic covariance matrices in the Berkson models of Poisson and logistic regressions are obtained.
Product Description
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Vitalii V. Holomozyi
Viktoriia P. Knopova
Kushnirenko Svitlana V.
Lukovych Olha V.
Sakhno Liudmyla M.
Shkliar Serhii V.
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2024-05-21
