2023-06-29 22:49:33 +02:00
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These are my notes on the lecture Probability Theory,
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taught by Prof.~\textsc{Chiranjib Mukherjee}
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2023-05-10 18:56:36 +02:00
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in the summer term 2023 at the University Münster.
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\begin{warning}
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This is not an official script.
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2023-06-29 22:49:33 +02:00
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The official lecture notes can be found on
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\href{https://sso.uni-muenster.de/LearnWeb/learnweb2/course/view.php?id=67595#coursecontentcollapse1}{Learnweb}.
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2023-05-10 18:56:36 +02:00
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\end{warning}
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These notes contain errors almost surely.
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2023-07-05 17:53:41 +02:00
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If you find some of them or want to improve something,
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please send me a message:\\
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2023-06-29 22:49:33 +02:00
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\texttt{notes\_probability\_theory@jrpie.de}.
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2023-05-10 18:56:36 +02:00
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2023-07-05 17:53:41 +02:00
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\paragraph{Topics of this lecture}
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2023-05-10 18:56:36 +02:00
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\begin{enumerate}[(1)]
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\item Limit theorems: Laws of large numbers and the central limit theorem for i.i.d.~sequences,
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\item Conditional expectation and conditional probabilities,
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\item Martingales,
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\item Markov chains.
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\end{enumerate}
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2023-07-13 14:26:03 +02:00
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This notes follow the way the material was presented in the lecture rather
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closely. Additions (e.g.~from exercise sheets)
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and slight modifications have been marked with $\dagger$.
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