Introduction to Stochastic Analysis
by Michael Roeckner
Publisher: Universitaet Bielefeld 2011
Number of pages: 98
From the table of contents: Introduction to Pathwise Ito-Calculus; (Semi-)Martingales and Stochastic Integration; Markov Processes and Semigroups - Application to Brownian Motion; Girsanov Transformation; Time Transformation.
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In 1999, Gian-Carlo Rota gave his famous course, Probability, at MIT for the last time. The late John N. Guidi taped the lectures and took notes which he then wrote up in a verbatim manner conveying the substance and the atmosphere of the course.
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We formulate conditions for convergence of Laws of Large Numbers and show its links with of parts mathematical analysis such as summation theory, convergence of orthogonal series. We present also various applications of Law of Large Numbers.
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