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

Material

• Material
  

  Material

  The main textbook of the course is

  Simo Särkkä and Arno Solin (2019). Applied Stochastic Differential Equations. Cambridge University Press.

  The book can be found in this link:

  http://users.aalto.fi/~ssarkka/pub/sde_book.pdf
  

  The examples codes of the book can be found here:

  https://github.com/AaltoML/SDE
  

  Lecture Slides can also be found down below as well as the YouTube videos and the quizzes.

  • ODE Basics

  • ODE Basics Quiz Kunskapstest
  • Lecture 1: Pragmatic Introduction to Stochastic Differential Equations
    

    
    

  • Lecture 1 Part 1: Stochastic differential equations URL
  • Lecture 1 Part 2: Stochastic processes in physics and engineering URL
  • Lecture 1 Part 3: Heuristic solutions of linear SDEs URL
  • Lecture 1 Part 4: Heuristic solutions of non-linear SDEs, and Summary URL
  • Lecture 1 Quiz Kunskapstest
  • Lecture 2: Itô Calculus and Stochastic Differential Equations
    

  • Lecture 2 Part 1: Stochastic integral of Itô URL
  • Lecture 2 Part 2: Itô formula URL
  • Lecture 2 Part 3: Solutions of linear and non-linear SDEs, Summary URL
  • Lecture 2 Quiz Kunskapstest
  • Lecture 3: Probability Distributions and Statistics of SDEs
    
    

  • Lecture 3 Part 1: Fokker-Planck-Kolmogorov Equation URL
  • Lecture 3 Part 2: Moments of SDEs URL
  • Lecture 3 Part 3: Statistics of linear SDEs, Markov, Markov Properties and Transition Densities SDEs, Summary URL
  • Lecture 3 Quiz Kunskapstest
  • Lecture 4: Numerical Solution of SDEs, Itô–Taylor Series, Gaussian Approximations
    

  • Lecture 4 part 1: Introduction, Gaussian approximations of non-linear SDEs URL
  • Lecture 4 part 2: Itô-Taylor series of SDEs URL
  • Lecture 4 part 3: Itô-Taylor series based numerical methods, Summary URL
  • Lecture 4 Quiz Kunskapstest
  • Lecture 5: Stochastic Runge–Kutta Methods
    

  • Lecture 5 part 1: Introduction, Runge–Kutta methods for ODEs URL
  • Lecture 5 part 2: Strong stochastic Runge–Kutta methods URL
  • Lecture 5 part 3: Weak stochastic Runge–Kutta methods, Summary URL
  • Lecture 5 Quiz Kunskapstest
  • Lecture 6: Bayesian Inference in SDE Models

  • Lecture 6: Bayesian Inference in SDE Models - Problem Formulation URL
  • Lecture 6: Discrete-time Bayesian filtering and Smoothing URL
  • Lecture 6: Continuous/Discrete-Time and Continuous Bayesian Filtering and Smoothing URL
  • Lecture 6 Quiz Kunskapstest
  • Lecture Slides Mapp