A Tutorial Introduction to Stochastic Differential Equations: Continuous-time Gaussian Markov Processes

Posted in Science on July 21, 2008


A Tutorial Introduction to Stochastic Differential Equations: Continuous-time Gaussian Markov Processes

Lecture content:

  • AR Processes: Discrete-time Gaussian Markov Processes
  • From discrete to continuous time
  • Vector processes
  • The Wiener Process
  • Discretized Wiener Process
  • Gaussian Processes
  • SDEs
  • Simulation of an SDE
  • Stochastic Integration
  • General form of a Diffusion process
  • Simple Examples
  • Infinitesimal moments
  • Stationary Processes
  • Fourier Analysis
  • Power spectrum of SDE
  • Vector OU process
  • Mean square differentiability
  • Relating Discrete-time and Sampled Continuous-time GMPs
  • Inference
  • Fokker-Planck Equations
  • Simple example: Wiener process with drift
  • Fokker-Planck Boundary Conditions
  • Parameter Estimation

Author: Chris Williams, University of Edinburgh

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Tags: Science, Lectures, Computer Science, Machine Learning, VideoLectures.Net, Markov Processes, Gaussian Processes