. "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"@en . "Nekone\u010Dn\u011Brozm\u011Brn\u00E9 stochastick\u00E9 syst\u00E9my" . . " invariant measure" . . . . "2015-01-22+01:00"^^ . . . "2009-04-22+02:00"^^ . "2009-12-31+01:00"^^ . "stochastic partial differential equations" . "1"^^ . "1"^^ . "GA201/07/0237" . "Projekt je zam\u011B\u0159en na v\u00FDzkum kvalitativn\u00EDch vlastnost\u00ED stochastick\u00FDch nekone\u010Dn\u011Brozm\u011Brn\u00FDch syst\u00E9m\u016F (speci\u00E1ln\u011B na \u0159e\u0161en\u00ED nekone\u010Dn\u011Brozm\u011Brn\u00FDch stochastick\u00FDch rovnic) a na v\u00FDzkum v teorii stochastick\u00E9ho \u0159\u00EDzen\u00ED takov\u00FDch syst\u00E9m\u016F. Bezprost\u0159edn\u00EDmi c\u00EDli jsou: 1. V\u00FDzkum existence, jednozna\u010Dnosti a vlastnost\u00ED trajektori\u00ED \u0159e\u0161en\u00ED nekone\u010Dn\u011Brozm\u011Brn\u00FDch stochastick\u00FDch rovnic, obzvl\u00E1\u0161t\u011B regularity a stability, speci\u00E1ln\u011B pro geometrick\u00E9 vlnov\u00E9 rovnice, rovnice v Banachov\u00FDch prostorech a rovnice s frakcion\u00E1ln\u00EDmi \u0161umy. 2. Asymptotick\u00E9 chov\u00E1n\u00ED a ergodicita pro markovsk\u00E9 a nemarkovsk\u00E9 stochastick\u00E9 rovnice. Tento v\u00FDzkum se zam\u011B\u0159\u00ED na metody pou\u017Eiteln\u00E9 na stochastick\u00E9 vlnov\u00E9 rovnice a rovnice ty\u010De a (v nemarkovsk\u00E9m p\u0159\u00EDpad\u011B) na rovnice, kde \u0159\u00EDd\u00EDc\u00EDm procesem je frakcion\u00E1ln\u00ED Brown\u016Fv pokyb. 3. Stochastick\u00E9 \u0159\u00EDzen\u00ED a p\u0159\u00EDslu\u0161n\u00E9 semiline\u00E1rn\u00ED Hamiltonovy-Jacobiho-Bellmanovy rovnice v nekone\u010Dn\u011Brozm\u011Brn\u00FDch prostorech: ergodick\u00E9 a adaptivn\u00ED \u0159\u00EDzen\u00ED. 4. V\u00FDzkum rovnic veden\u00ED tepla na p\u0159\u00EDmce s Wrightov\u00FDm-Fisherov\u00FDm nebo v\u011Btv\u00EDc\u00EDm \u0161umem a" . "0"^^ . . "18"^^ . "http://www.isvav.cz/projectDetail.do?rowId=GA201/07/0237"^^ . "18"^^ . "Infinite dimensional stochastic systems"@en . . " ergodicity" . . "."@en . . . . "Projekt p\u0159inesl v\u00FDznamn\u00E9 v\u00FDsledky zejm\u00E9na o existenci a regularit\u011B \u0159e\u0161en\u00ED stochastick\u00FDch evolu\u010Dn\u00EDch rovnic a o \u0159e\u0161en\u00ED \u00FAloh optim\u00E1ln\u00EDho \u0159\u00EDzen\u00ED pro evolu\u010Dn\u00ED rovnice. V\u00FDsledky byly publikov\u00E1ny nebo jsou p\u0159ijaty k publikaci v presti\u017En\u00EDch mezin\u00E1rodn\u00EDch \u010Dasopis"@cs . . . . . . "stochastic partial differential equations; invariant measure; ergodicity; fractional Brownian motion"@en . "2007-01-01+01:00"^^ .