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.

  
  

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    Applied stochastic differential equations File

    PDF document
  • ODE Basics

  • ODE Basics Self-Study Task (DL 30.10.2018) Page
  • ODE Basics Quiz
  • Lecture 1 (DL 1.11.2018): 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 6.11.2018): 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 TBA): 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 TBA): 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 TBA): 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 TBA)

  • 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 TBA)