EEA-EV - Vaihtuvasisältöinen opinto, Applied Stochastic Differential Equations, 01.07.2020-04.09.2020

Topic outline

• Schedule and organization
  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:

  • https://github.com/AaltoML/SDE/blob/master/matlab/ch04_ex05_ou_process.m

  • https://github.com/AaltoML/SDE/blob/master/matlab/ch04_fig01_brownian_motion.m 

  • 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:

  • https://github.com/AaltoML/SDE/blob/master/matlab/ch08_ex11_ode_solvers.m

  • https://github.com/AaltoML/SDE/blob/master/matlab/ch09_ex07_gaussian_approximation.m

  • 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:

  • https://github.com/AaltoML/SDE/blob/master/matlab/ch08_ex06_weak_itotaylor.m

  • https://github.com/AaltoML/SDE/blob/master/matlab/ch09_ex06_linearizations_for_benes.m

  • 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:

  • https://github.com/AaltoML/SDE/blob/master/matlab/ch10_ex17_benes_daum_ekf_erts.m

  • https://github.com/AaltoML/SDE/blob/master/matlab/ch10_ex19_ou_filtering_smoothing.m 

  • 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:

  • https://github.com/AaltoML/SDE/blob/master/matlab/ch11_ex05_ou_parameter_estimation.m