Registration Number
0223U001948,
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
06-02-2023
Organization
Taras Shevchenko National University of Kyiv
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The object of research is random processes and fields, stochastic differential equations, financial markets, equations with random initial conditions, processes with random time change, models of regressions with errors.
The purpose of the work is the development of the theory of fractional and Levy type processes, risk processes, investigation of stochastic differential equations and equations with random initial conditions which model physical and financial processes, estimation of regression models with measurements errors and models of mixtures.
The methods of research are the analytical methods of probability theory and mathematical statistics, methods of stochastic analysis, statistical modeling of random processes and fields, theory of optimization and numerical methods.
The main research results of the work are:
Connection between the standard (or fractional) Cox-Ingersoll-Ross and reflected OrnsteinUhlenbeck processes was established. The formulas were stated for the reflection function, boudns of reflection were found for the drift coefficient. The results were applied for investigation of financial markets with stochastic volatility. For stochastic differential equations with the Volterra-Levy additive noise, the conditions for the existence and uniqueness of the solution and its main properties were obtained. For Volterra-Gauss processes, the existence and uniqueness of the solution were proved under the conditions of sublinear growth and Hölder condition on the shift coefficient. For Volterra-Gauss processes with three-parameter kernels, the inverse Molchan-Golos representation was justificated, asymptotics of trajectories was stated, values of paprameters were investigated for which the processes had short or long memory. The behavior of densities of stable type processes was studied under conditions
allowing the drift domination. Caloric estimates for the norm of operator semigroup in Besovand Triebel-Lizorkin spaces were stated.
Product Description
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Bodnarchuk Iryna M.
Knopova Victoria P.
Maiboroda Rostyslav Ye.
Sakhno Liudmyla M.
Shkliar Sergiy V.
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2023-02-06
