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Infinite dimensional stochastic systems

Begin
End
Agency
GACR
Identification Code
GA201/07/0237
Project Type (EU)
other
Publications ÚTIA
Web
Abstract
The project is aimed at investigating qualitative properties of stochastic infinite dimensional systems (in particular, of solutions to infinite dimensional stochastic equations) and at research in infinite dimensional stochastic control theory. The moreimmediate aims are: 1. Investigation of existence, uniqueness and pathwise properties of solutions to infinite dimensional stochastic equations, in particular of the path regularity and stability, especially for geometric wave equations, equations in Banach spaces and equations driven by fractional noises. 2. Large time behaviour and ergodicity for Markovian and non-Markovian stochastic equations. This research will be focused on methods applicable to stochastic wave and beam equations and (in the non-Markovian case) on equations where the driving process is a fractional Brownian motion. 3. Infinite dimensional stochastic control and the associated semilinear Hamilton-Jacobi-Bellman equations in infinite dimensions: ergodic and adaptive control
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