EEA-EV - Course with Varying Content Applied Stochastic Differential Equations , 31.10.2016-17.12.2016

Materials

• Materials
  

  Materials

  The main textbook of the course is

  • Simo Särkkä and Arno Solin (2014). Applied Stochastic Differential Equations. https://users.aalto.fi/~ssarkka/course_s2014/sde_course_booklet.pdf

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

  • 3.11.2016 - Lecture 0: Applied Stochastic Differential Equations Course in 2016 (PDF)
  • 3.11.2016 - Lecture 1: Pragmatic Introduction to Stochastic Differential Equations (PDF)
    
  • 10.11.2016 - Lecture 2: Itô Calculus and Stochastic Differential Equations (PDF)
    
  • 17.11.2016 - Lecture 3: Probability Distributions and Statistics of SDEs (PDE)
    
  • 24.11.2016 - Lecture 4: Numerical Solution of SDEs, Itô–Taylor Series, Gaussian Approximations (PDF)
    
  • 1.12.2016 - Lecture 5: Stochastic Runge–Kutta Methods (PDF)
    
  • 8.12.2016 - Lecture 6: Bayesian Inference in SDE Models (PDF)
    

  
  

  Additional ODE introduction material together with a quiz is provided as well, and they are recommended to be studied and completed by 3.11.2016, but they are not compulsory.
  

  • ODE Basics

  • ODE Basics Self-Study Task (DL 3.11.2016 at 14) Page
  • ODE Basics Quiz
  • Course Intro Lecture (DL 3.11.2016 at 14)

  • Lecture 0: Applied Stochastic Differential Equations Course in 2016 URL
  • Lecture 1 (DL 3.11.2016 at 14): 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
  • Lecture 2 (DL 10.11.2016 at 14): 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
  • Lecture 3 (DL 17.11.2016 at 14): 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
  • Lecture 4 (DL 24.11.2016 at 14): 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
  • Lecture 5 (DL 1.12.2016 at 14): 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
  • Lecture 6 (DL 8.12.2016 at 14)

  • 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
  • End-of-course feedback (DL 8.1.2018)