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1 = Stochastic methods in physics and biology, spring 2014 =
2
3 === Lecturer ===
4
5 [[Paolo Muratore-Ginanneschi>>doc:mathstatHenkilokunta.Muratore-Ginanneschi, Paolo]]
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7 [[Matteo Marcozzi>>doc:mathstatHenkilokunta.Home.Matteo Marcozzi.WebHome]] (assistant)
8
9 === Scope ===
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11 10 sp.
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13 The aim of the course is to introduce the basic concepts of the theory of stochastic differential equations needed in applications (applied mathematics, physics and biology).
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15 === Prerequisites ===
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17 === Type ===
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19 Advanced studies
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21 === Prerequisites ===
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23 The course is intended for undergraduate students of mathematics, physics. Prior courses in advanced calculus and linear algebra are required (Diff.Int. 1-2 and Lineaarialgebra 1, or Mapu 1-2).
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25 === Lectures ===
26
27 Weeks 4-9 and 11-18, Monday 14-16 in room D123, and Friday 14-16 in room C123.
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29 Easter holiday 17.-23.4.
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31 === Lecture Notes ===
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33 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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35 |=(((
36 Lectures 1-10
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38 Lectures 10-20
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41 [[Lecture 01>>attach:lecture_01.pdf]]: Probability spaces and random variables (v 11.02)
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43 [[Lecture 11>>attach:lecture_11.pdf]]: Karhunen–Loève representation of the Brownian motion
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46 [[Lecture 02:>>attach:lecture_02.pdf]][[:>>attach:lecture_02.pdf]] Independence, conditional expectations and inequalities (v 11.02)
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48 [[Lecture 12>>attach:lecture_12.pdf]]: Calculus for paths of finite quadratic variation (v 04.04)
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51 [[Lecture 03>>attach:lecture_03.pdf]]: Classical limit theorems (v 11.02)
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53 [[Lecture 13>>attach:lecture_13.pdf]]: Ito integrals (v. 08.04)
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56 [[Lecture 04>>attach:lecture_04.pdf]]: Sequences of random variables and martingales (v 07.02)
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58 [[Lecture 14>>attach:lecture_14.pdf]]: Stratonovich integral, stochastic differential equations (v 08.04)
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61 [[Lecture 05>>attach:lecture_05.pdf]]: From Bernoulli variables to Random Walk (v 11.02)
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66 [[Lecture 06>>attach:lecture_06.pdf]]: Continuous Time Random Walks and Montroll-Weiss equation
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71 [[Lecture 07>>attach:lecture_07.pdf]]: Asymptotic analysis of the Montroll–Weiss process
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76 [[Lecture_08>>attach:lecture_08.pdf]]: Girsanov formula for continuous Markov Processes
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81 [[Lecture 09>>attach:lecture_09.pdf]]: Kolmogorov axioms and Kolmogorov–Chentsov theorem (v. 21.03)
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86 [[Lecture 10>>attach:lecture_10.pdf]]: Brownian motion (v. 21.03)
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90
91 === Exams ===
92
93 === Bibliography ===
94
95 1. Schuss Z., "Theory and Applications of Stochastic Processes: An Analytical Approach" (Springer), 2010, 170, 468.
96 1. (((
97 (% class="_mce_tagged_br" %)
98 Gardiner C. W., "Handbook of stochastic methods for physics, chemistry and the natural sciences" (Springer), 1994, 13, 442.
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100 1. (((
101 (% class="_mce_tagged_br" %)
102 Evans L. C., "An Introduction to Stochastic Differential Equations", Berkeley lecture notes.
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104 1. (((
105 (% class="_mce_tagged_br" %)
106 van Handel R., "Stochastic Calculus and Stochastic Control", CalTech lecture notes (2007).
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108 1. (((
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110 Klebaner F. C., "Introduction to stochastic calculus with applications" (Imperial College Press), 2005, 416.
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112 1. (((
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114 Higham D. J., "An algorithmic introduction to numerical simulation of stochastic differential equations", SIAM Review, Education Section, 43, 2001, 525-546. (Link to Higham's publications page.)
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116
117 === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57072||shape="rect"]] ===
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119
120 Did you forget to register? [[ What to do?>>doc:mathstatOpiskelu.Kysymys4]]
121
122 === Exercise session ===
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125 Group
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127 Day
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129 Time
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131 Place
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133 Lecturer
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136 1.
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138 Friday
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140 16-18
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142 B321
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144 [[Matteo Marcozzi>>doc:mathstatHenkilokunta.Home.Matteo Marcozzi.WebHome]]
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148 Exercise Notes
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153 (% class="confluence-link" %)Notes 01
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158 (% class="confluence-link" %)Notes 02
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163 (% class="confluence-link" %)Exercise Session[[07>>attach:Exercise_session_7.pdf]]
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168 (% class="confluence-link" %)Exercise Session 08
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