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Téma:
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Matematika
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Pályázat:
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TÁMOP 0027
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Ismertető:
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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.
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Szerzők:
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Tóth Bálint
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Kulcsszavak:
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limit theorems
infinitely divisible distributions
Lévy–Khinchin formula
Ergodic theorems
stable laws
Erdős–Kac theorem
characteristic functions
Lindeberg's theorem
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Szakok:
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MSC Matematikusoknak -> Matematikus MSC -> Határeloszlás tételek a valószínűségszámításban
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Ajtay János
Limit theorems of Probability Theory