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1 = Stochastic methods for physics and biology, spring 2012 =
2
3 === Lecturer ===
4
5 [[Paolo Muratore-Ginanneschi>>doc:mathstatHenkilokunta.Muratore-Ginanneschi, Paolo]]
6
7 === Scope ===
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9 10 cu.
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11 === Type ===
12
13 Advanced studies
14
15 === Prerequisites ===
16
17 === Lectures ===
18
19 === Lecture Notes ===
20
21 The lecture notes cover and sometimes integrate the material expounded in the lections. They also give bibliographic references for the same topics.
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24 Lectures 1-10
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26 Lectures 10-20
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29 [[Lecture_01>>attach:lecture_01.pdf]] Review of Probability: random variables and their expectations (rev 04.02)
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31 [[Lecture_11>>attach:lecture_11.pdf]] Karhunen–Loève representation of the Brownian motion
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34 [[Lecture_02>>attach:lecture_02.pdf]] Review of Probability: classical theorems (part I) (rev 30.01)
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36 [[Lecture_12>>attach:lecture_12.pdf]] Ito and Stratonovich stochastic integrals
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39 [[Lecture_03>>attach:lecture_03.pdf]] Review of Probability: classical theorems (part II) (rev 04.02)
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41 [[Lecture_13>>attach:lecture_13.pdf]] Stochastic differential equations
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44 [[Lecture_04>>attach:lecture_04.pdf]] Probability and Classical Statistical Mechanics (rev 07.02)
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46 [[Lecture_14>>attach:lecture_14.pdf]] Backward Master equation and backward Kolmogorov equation
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49 [[Lecture_05>>attach:lecture_05.pdf]] Random Walk (rev 13.03)
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51 [[Lecture_15>>attach:lecture_15.pdf]] Forward Master equation and forward Kolmogorov equation
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54 [[Lecture_06>>attach:lecture_06.pdf]] Conditional expectation and Martingales (rev 13.03)
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56 [[Lecture_16>>attach:lecture_16.pdf]] Exit time statistics (rev 20.04)
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59 [[Lecture_07>>attach:lecture_07.pdf]] Markov jump processes (rev 01.03)
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61 [[Lecture_17>>attach:lecture_17.pdf]] Diffusions in one dimension: analysis of boundary conditions
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64 [[Lecture_08>>attach:lecture_08.pdf]] Continuity of paths, Kolmogorov-Chentsov theorem
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66 [[Lecture_18>>attach:lecture_18.pdf]] Hamilton-Bellman-Jacobi equation
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69 [[Lecture_09>>attach:lecture_09.pdf]] Ito lemma for paths of finite quadratic variation
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74 [[Lecture_10>>attach:lecture_10.pdf]] Brownian Motion
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78
79 === Exams ===
80
81 === Description ===
82
83 The aim of the course is to introduce the basic concepts of the theory
84 of stochastic differential equations (SDE) needed in applications (applied
85 mathematics, physics and biology). In particular we will illustrate
86 methods of qualitative, asymptotic and numerical analysis of SDE.
87 Among the scopes of the course is also to provide an elementary
88 introduction to stochastic control and filtering theory.
89
90 === Bibliography ===
91
92 1. Gardiner, C. W. Handbook of stochastic methods for physics, chemistry and the natural sciences Springer, 1994, 13, 442
93 1. L.C. Evans, "An Introduction to Stochastic Differential Equations", Berkeley lecture notes.
94 1. R. van Handel, "Stochastic Calculus and Stochastic Control", CalTech lecture notes (2007)
95 1. D.J. Higham, "An algorithmic introduction to numerical simulation of stochastic differential equations" SIAM Review, Education Section, 43, 2001, 525-546. (Link to Higham's publications page.)
96
97 === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57357||shape="rect"]] ===
98
99 Did you forget to register? [[What to do>>doc:mathstatOpiskelu.Kysymys4]].
100
101 === Exercise groups ===
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104 Group
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106 Day
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108 Time
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110 Place
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112 Instructor
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115 1.
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