Téma: Matematika
Pályázat: TÁMOP 0027
Ismertető: This course is taught regularly for those MSc students of mathematics at TU Budapest who chose stochastics as topics of specialization. It is assumed that students have a solid background in probability theory (with measure theoretic foundations) and analysis. The following material covers: ergodic theorems (von Neumann's and Birkhoff's); limit theorems “with bare hands”: Levy's arcsine laws, sojourn time and local time of 1d random walk; the method of moments with applications; the method of characteristic functions: Lindeberg's theorem with applications, Erdős–Kac theorem (CLT for the number of prime divisors), various other applications; stable laws and stable limits with applications; infinitely divisible distributions, Lévy–Khinchin formula and elements of Lévy processes. With lots of problems for solution and applications.
Szerzők: Tóth Bálint
Kulcsszavak: limit theorems
infinitely divisible distributions
Lévy–Khinchin formula
Ergodic theorems
stable laws
Erdős–Kac theorem
characteristic functions
Lindeberg's theorem
Szakok: MSC Matematikusoknak -> Matematikus MSC -> Határeloszlás tételek a valószínűségszámításban