"http://www.isvav.cz/projectDetail.do?rowId=GA201/98/1454"^^ . . "V\u00FDsledky lze rozd\u011Blit do 3 skupin: a) v\u00FDzkum kvalitativn\u00EDch vlastnost\u00ED trajektori\u00ED \u0159e\u0161en\u00ED evolu\u010Dn\u00EDch rovnic, b) v\u00FDzkum limitn\u00EDch vlastnost\u00ED Markovsk\u00FDch proces\u016F definovan\u00FDch stochastick\u00FDmi evolu\u010Dn\u00EDmi rovnicemi, c) \u0159\u00EDzen\u00ED syst\u00E9m\u016F pomoc\u00ED stochastick\u00FDch evol"@cs . . . "0"^^ . . "Bude vy\u0161et\u0159ov\u00E1no asymptotick\u00E9 chov\u00E1n\u00ED stochastick\u00FDch evolu\u010Dn\u00EDch rovnic, se zvl\u00E1\u0161tn\u00EDm z\u0159etelem jednak k asymptotick\u00E9mu chov\u00E1n\u00ED (speci\u00E1ln\u011B stabilit\u011B) trajektori\u00ED, jednak k limitn\u00EDmu chov\u00E1n\u00ED markovsk\u00E9ho procesu definovan\u00E9ho rovnic\u00ED (nap\u0159. existence a jednozna\u010Dnost invariantn\u00ED m\u00EDry, ergodi\u010Dnost a mixing procesu, konvergence \u0159e\u0161en\u00ED v distribuci). V\u00FDsledky budou aplikov\u00E1ny na stochastick\u00E9 evolu\u010Dn\u00ED rovnice uva\u017Eovan\u00E9 v matematick\u00E9 biologii a fyzice (rovnice popula\u010Dn\u00ED dynamiky, stochastick\u00E9 hydrodynamiky, stochastick\u00E9 rovnice s nehomogenn\u00ED okrajovou podm\u00EDnkou a jin\u00E9). Bude studov\u00E1no ergodick\u00E9 a adaptivn\u00ED \u0159\u00EDzen\u00ED pro stochastick\u00E9 evolu\u010Dn\u00ED syst\u00E9my a budou zkoum\u00E1ny i s t\u00EDm souvisej\u00EDc\u00ED Hamilton-Jacobiho rovnice v nekone\u010Dn\u011B rozm\u011Brn\u00FDch prostorech." . "Qualitative theory of stochastic evolutions"@en . . . "GA201/98/1454" . "Asymptotic behaviour of solutions to stochastic evolution equations will be investigated with particular attention paid to the pathwise asymptotics(especially stability) and to long-time behaviour of the Markov processes induced by the stochastic evolution equations, like existence and uniqueness of an invariant measure, ergodicity and the mixing property of the process and convergence in law of solutions. The results will be applied to stochastic equation arising in mathematical biology and physics (equations of population dynamics, equations arising in stochastic hydrodynamics, stochastic non-homogenous boundary value problems and others). Stochastic ergodic control and adaptive control problems will be studied for stochastic evolutionary systems and related infinite-dimensional Hamilton-Jacobi equations will be investigated."@en . "5"^^ . "Kvalitativn\u00ED teorie stochastick\u00FDch evolu\u010Dn\u00EDch rovnic" . "5"^^ . "0"^^ . . . "1"^^ . . . . . . .