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Description
  • The project studies the methods of martingale approximations and has two main goals. First of them is use of the methods of martingale approximations to derive new conditions for the central limit theorem, the invariance principle and the law of iterated logarithm for nonadapted processes with nonlinear growth of variances. The second aim is use of the same methods for deriving condition for asymptotic normality of U-statistics. (en)
  • Navrhovaný projekt se bude zabývat technikami martingalových aproximací stacionárních náhodných procesů. Pomocí těchto aproximací budou v rámci projektu hledány podmínky pro stacionární neadaptované procesy s nelineárním růstem rozptylu, za nichž platí centrální limitní věta, princip invariance, zákon iterované logaritmu. Druhým cílem je pomocí technik martingalových aproximací najít podmínky pro asymptotickou normalitu U-statistik.
Title
  • Martingale approximations and U-statistics (en)
  • Martingalové aproximace a U-statistiky
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  • GPP201/11/P164
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  • stationary processes central limit theorem martingale approximation (en)
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