EEA-EV - Vaihtuvasisältöinen opinto, Applied Stochastic Differential Equations, 01.07.2020-04.09.2020
This course space end date is set to 04.09.2020 Search Courses: EEA-EV
Topic outline
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The contact sessions (Wednesdays 14:15-16:00 in course slack) are discussion sessions of lecture and homework exercises that the students have (preferably) solved beforehand. Recall that the lectures/materials must be studied before the sessions and the quizzes must be completed before them as well! The homework exercises are related to the lectures and hence it is advisable to watch the videos first and then do the exercises. There are two deadlines for returning the exercise answers:
Rounds 1-4 on 31.7.
Rounds 5-8 on 28.8.
At least 50% (12/24) of homework exercises must be completed and completing at least 75% (18/24) of exercises gives a +1 grade increase to the exam. Finishing all quizzes gives one extra exercise point.
The contact session topics are given in the following, the exercises are from the coursebook:
1.7.2020 - Self-study task: ODE Basics (ch. 2)
Read Chapter 2 in the coursebook
ODE Basics Quiz is mandatory, deadline 5.7.2020, no exercises this time
Useful example code: https://github.com/AaltoML/SDE/blob/master/matlab/ch02_ex09_numerical_solution_of_odes.m
8.7.2020 - Lecture 1: Pragmatic Introduction to Stochastic Differential Equations (ch. 3)
Lecture Slides
Lecture 1 Part 1: Stochastic differential equations
Lecture 1 Part 2: Stochastic processes in physics and engineering
Lecture 1 Part 3: Heuristic solutions of linear SDEs
Lecture 1 Part 4: Heuristic solutions of non-linear SDEs, and Summary
Lecture 1 Quiz
Exercise round 1: 3.1, 3.2, 3.3
Useful example codes:
https://github.com/AaltoML/SDE/blob/master/matlab/ch03_ex07_time_varying_oscillator.m
https://github.com/AaltoML/SDE/blob/master/matlab/ch03_ex10_stochastic_spring_model.m
https://github.com/AaltoML/SDE/blob/master/matlab/ch03_fig02_two_views_of_brownian_motion.m
https://github.com/AaltoML/SDE/blob/master/matlab/ch03_fig10_white_noise.m
15.7.2020 - Lecture 2: Itô Calculus and Stochastic Differential Equations (ch. 4)
Lecture Slides
Lecture 2 Part 1: Stochastic integral of Itô
Lecture 2 Part 2: Itô formula
Lecture 2 Part 3: Solutions of linear and non-linear SDEs, Summary
Lecture 2 Quiz
Exercise round 2: 4.1, 4.2, 4.6
Useful example codes:
22.7.2020 - Lecture 3: Probability Distributions and Statistics of SDEs (ch. 5)
Lecture Slides
Lecture 3 Part 1: Fokker-Planck-Kolmogorov Equation
Lecture 3 Part 2: Moments of SDEs
Lecture 3 Part 3: Statistics of linear SDEs, Markov, Markov Properties and Transition Densities SDEs, Summary
Lecture 3 Quiz
Exercise round 3: 5.1, 5.2, 5.4
29.7.2020 - Self-study task: Linear stochastic differential equations (ch. 6)
Read Chapter 6 in the coursebook
Exercise round 4: 6.1, 6.3, 6.8
5.8.2020 - Lecture 4: Numerical Solution of SDEs, Itô–Taylor Series, Gaussian Approximations (ch. 8 & 9)
Lecture Slides
Lecture 4 part 1: Introduction, Gaussian approximations of non-linear SDEs
Lecture 4 part 2: Itô-Taylor series of SDEs
Lecture 4 part 3: Itô-Taylor series based numerical methods, Summary
Lecture 4 Quiz
Exercise round 5: 8.1, 8.2, 9.1
Useful example codes:
12.8.2020 - Lecture 5: Stochastic Runge–Kutta Methods (ch. 8)
Lecture Slides
Lecture 5 part 1: Introduction, Runge–Kutta methods for ODEs
Lecture 5 part 2: Strong stochastic Runge–Kutta methods
Lecture 5 part 3: Weak stochastic Runge–Kutta methods, Summary
Lecture 5 Quiz
Exercise round 6: 8.3, 8.4, 8.5
Useful example codes:
19.8.2020 - Lecture 6: Bayesian Inference in SDE Models (ch. 10)
Lecture Slides
Lecture 6: Bayesian Inference in SDE Models - Problem Formulation
Lecture 6: Discrete-time Bayesian filtering and Smoothing
Lecture 6: Continuous/Discrete-Time and Continuous Bayesian Filtering and Smoothing
Lecture 6 Quiz
Exercise round 7: 10.2, 10.4, 10.5
Useful example codes:
26.8.2020 - Self-study task: Parameter estimation in SDE models (ch. 11)
Read Chapter 11 in the coursebook
Exercise round 8: 11.1, 11.4, 11.9
Useful example codes: