Wiki source code of Probabilistic approximations, spring 2015
Last modified by gasbarra@helsinki_fi on 2024/03/27 10:24
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1 | = Probabilistic approximations, spring 2015 = | ||
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3 | === Lecturer === | ||
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5 | [[Ehsan Azmoodeh>>url:http://math.uni.lu/~~azmoodeh/||shape="rect"]], University of Luxembourg | ||
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7 | === Scope === | ||
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9 | 3 sp. | ||
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11 | === Type === | ||
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13 | Advanced studies | ||
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15 | === Prerequisites === | ||
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17 | A basic knowledge about probability theory in the level of the book [[Probability Essentials>>url:http://www.amazon.com/Probability-Essentials-Jean-Jacod/dp/3540438718||shape="rect"]] by Jean Jacod and Philip Protter. Some knowledge about Malliavin calculus will help a lot, but it is not necessary, the essential ingredients from Malliavin Calculus will be discussed in the lectures. | ||
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19 | === Content === | ||
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21 | ((( | ||
22 | The aim of the course is to combine two probabilistic techniques, namely the Malliavin calculus and Stein's method to study the Gaussian and non-Gaussian approximations of non-linear functionals of infinite-dimensional Gaussian fields. One of the main objectives of the course is to prove an interesting result in modern theory of probabilistic approximations known nowadays as the fourth moment theorem. | ||
23 | ))) | ||
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25 | === Lectures === | ||
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27 | On mondays March 23, April 27 and May 25 at 12-14 in room CK107, | ||
28 | on thursdays March 26 at 15-17, April 30 at 14-16 and May 28 at 15-17 in room C129 | ||
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30 | === Exercise classes === | ||
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32 | On friday March 27 at 10-12 in room B321, on Thursday April 30 at 12-14 in B321, and on wednesday May 27 at 10-12 in B322. | ||
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34 | [[Exercise sheet 1>>attach:Ex-sheet-1.pdf]] (27.3) [[Exercise sheet 2>>attach:Ex-sheet-2.pdf]] (30.4) [[Exercise sheet 3>>attach:Ex-sheet-3.pdf]] (29.5) | ||
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36 | === Exams === | ||
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38 | To pass the course, students have to solve the exercises assigned during each week and to write an home exam at the end of the cycle of lectures. | ||
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42 | === Bibliography === | ||
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44 | [[Lecture notes 1-2,>>attach:LectureNote-1-2.pdf]] [[Lecture Note 3>>attach:LectureNote-3.pdf]] | ||
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46 | Book: Nourdin Ivan, Peccati Giovanni: Normal Approximations with Malliavin Calculus: From Stein's Method to Universality. Cambridge Tracts in Mathematics, 2012. | ||
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50 | === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57072||shape="rect"]] === | ||
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52 | Did you forget to register? [[ What to do?>>doc:mathstatOpiskelu.Kysymys4]] | ||
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