# 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*