EEA-EV - Course with Varying Content, Applied Stochastic Differential Equations, 29.10.2018-15.12.2018

Materials

• Materials
  

  Materials

  The main textbook of the course is

  Simo Särkkä and Arno Solin. Applied Stochastic Differential Equations. Cambridge University Press (in press). This is available in PDF form below.

  The lecture videos, lecture slides, and additional information are provided below on this page. The lecture topics must be studied and their homeworks and quizzes completed (preferably) before the corresponding contact sessions as follows:

  • 30.10.2018 - Lecture 1: Pragmatic Introduction to Stochastic Differential Equations (PDF)
    
  • 6.11.2018 - Lecture 2: Itô Calculus and Stochastic Differential Equations (PDF)
    
  • 13.11.2018 - Lecture 3: Probability Distributions and Statistics of SDEs (PDF)
    
  • 20.11.2018 - Lecture 4: Numerical Solution of SDEs, Itô–Taylor Series, Gaussian Approximations (PDF)
    
  • 27.11.2018 - Lecture 5: Stochastic Runge–Kutta Methods (PDF)
    
  • 4.12.2018 - Lecture 6: Bayesian Inference in SDE Models (PDF)
  • 11.12.2018 - Project work information event

  
  

  Additional ODE introduction material together with a quiz is provided as well, and they are recommended to be studied and completed by the first contact session, but they are not compulsory.

  
  

  • Rajoitettu Ei saatavilla, jollei: Kenttä Käyttäjätunnus sisältää (käytä: aalto.fi) on aalto.fi

    Applied stochastic differential equations Tiedosto

    PDF document
  • ODE Basics

  • ODE Basics Self-Study Task (DL 30.10.2018) Sivu
  • ODE Basics Quiz Quiz -tehtävä
  • Lecture 1 (DL 1.11.2018): Pragmatic Introduction to Stochastic Differential Equations
    

    
    

  • Lecture 1 Part 1: Stochastic differential equations Verkko-osoite
  • Lecture 1 Part 2: Stochastic processes in physics and engineering Verkko-osoite
  • Lecture 1 Part 3: Heuristic solutions of linear SDEs Verkko-osoite
  • Lecture 1 Part 4: Heuristic solutions of non-linear SDEs, and Summary Verkko-osoite
  • Lecture 1 Quiz Quiz -tehtävä
  • Lecture 2 (DL 6.11.2018): Itô Calculus and Stochastic Differential Equations
    

  • Lecture 2 Part 1: Stochastic integral of Itô Verkko-osoite
  • Lecture 2 Part 2: Itô formula Verkko-osoite
  • Lecture 2 Part 3: Solutions of linear and non-linear SDEs, Summary Verkko-osoite
  • Lecture 2 Quiz Quiz -tehtävä
  • Lecture 3 (DL TBA): Probability Distributions and Statistics of SDEs
    
    

  • Lecture 3 Part 1: Fokker-Planck-Kolmogorov Equation Verkko-osoite
  • Lecture 3 Part 2: Moments of SDEs Verkko-osoite
  • Lecture 3 Part 3: Statistics of linear SDEs, Markov, Markov Properties and Transition Densities SDEs, Summary Verkko-osoite
  • Lecture 3 Quiz Quiz -tehtävä
  • Lecture 4 (DL TBA): Numerical Solution of SDEs, Itô–Taylor Series, Gaussian Approximations
    

  • Lecture 4 part 1: Introduction, Gaussian approximations of non-linear SDEs Verkko-osoite
  • Lecture 4 part 2: Itô-Taylor series of SDEs Verkko-osoite
  • Lecture 4 part 3: Itô-Taylor series based numerical methods, Summary Verkko-osoite
  • Lecture 4 Quiz Quiz -tehtävä
  • Lecture 5 (DL TBA): Stochastic Runge–Kutta Methods
    

  • Lecture 5 part 1: Introduction, Runge–Kutta methods for ODEs Verkko-osoite
  • Lecture 5 part 2: Strong stochastic Runge–Kutta methods Verkko-osoite
  • Lecture 5 part 3: Weak stochastic Runge–Kutta methods, Summary Verkko-osoite
  • Lecture 5 Quiz Quiz -tehtävä
  • Lecture 6 (DL TBA)

  • Lecture 6: Bayesian Inference in SDE Models - Problem Formulation Verkko-osoite
  • Lecture 6: Discrete-time Bayesian filtering and Smoothing Verkko-osoite
  • Lecture 6: Continuous/Discrete-Time and Continuous Bayesian Filtering and Smoothing Verkko-osoite
  • Lecture 6 Quiz Quiz -tehtävä
  • End-of-course feedback (DL TBA)