# Stochastic Processes

## Content

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## Description

#### Module Overview: Stochastic Processes (semester 2)

The first three lectures of the second semester are devoted to Markov processes. These form the basis of most probabilistic modelling of physical and other processes. Elegant descriptions of their long-term behaviour make them particularly useful. They have further important applications in statistical inference.

A further three lectures are devoted to the stochastic modelling and simulation of physical processes. With the availability of extensive computing power, simulation techniques have become an important probabilistic and statistical tool, and there is now an extensive theory of probabilistic simulation. One of these lectures focuses on the interplay between probability theory and graph theory.

The final four lectures are concerned with continuous-time stochastic processes and stochastic calculus. Again there are important applications to the modelling of physical and natural processes.

##### Lecturers:

- Mateusz Majka (Heriot-Watt University)
- Sergey Foss (Heriot-Watt University)
- Yvain Bruned (University of Edinburgh)
- Istvan Gyongy (University of Edinburgh)

**Assessment**

This module is assessed by two written assignments (to be set at least two weeks before the deadline), to be submitted by 23 February 2021 (Assignment 1) and 30 March 2021 (Assignment 2). These dates will be confirmed nearer the time. Solutions to at least one of the assignments should be produced using LaTeX.

##### Prerequisites

Elements of mathematical analysis, linear algebra and combinatorics at undergraduate level. Probability theory, either at undergraduate level or from the Foundations of Probability module.