t theorems of Probability Theory
Tóth Bálint
limit theorems
infinitely divisible distributions
Lévy–Khinchin formula
Ergodic theorems
stable laws
Erdős–Kac theorem
characteristic functions
Lindeberg's theorem
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.
Budapesti Műszaki és Gazdaságtudományi Egyetem Természettudományi Kar
Budapesti Műszaki és Gazdaságtudományi Egyetem Természettudományi Kar
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http://tankonyvtar.ttk.bme.hu/pdf/46.pdf
2011-06-30
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Tóth Bálint
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