Institute of Information Theory and Automation

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Stochastic systems in infinite dimensions

Agency: 
GACR
Identification Code: 
GA22-12790S
Start: 
2022-01-01
End: 
2024-12-31
Project Focus: 
teoretický
Project Type (EU): 
other
Abstract: 
The project is aimed at research in the field of stochastic systems in infinite dimensions, especially stochastic partial differential equations with non-Markovian and non-Gaussian noise terms. The main goal is to study basic properties thereof, in particular, the existence, uniqueness and regularity in time and space. Also, dynamic and asymptotic properties of solutions will be investigated, like stability, ergodicity, stabilization of equations by noise and existence of random attractors. Additionally, problems of parameter identification and control for such systems will be studied. Research of stochastic flows will be also included. General results will be applied especially to stochastic linear, bilinear and semilinear equations, like e.g. reaction-diffusion equations or NS equations. Special attention will be paid to stochastic models of geophysical fluid dynamics. As typical examples of random perturbations, Volterra processes (both Gaussian and non-Gaussian) may be considered (for example, fractional Brownian motion and the Rosenblatt process).
Publications ÚTIA: 
list
2022-12-02 12:14