# Unit information: Stochastic Processes in 2016/17

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Unit name Stochastic Processes MATHM6006 10 M/7 Teaching Block 1B (weeks 7 - 12) Professor. Balint Toth Not open MATH36204 Martingale Theory and Applications 3 or MATHM6204 Martingale Theory and Applications 4. Background in PDE's helpful but not essential None School of Mathematics Faculty of Science

## Description

Unit aims

The aim of the unit is to introduce theory of Brownian motions, in particular, how to construct it from random walks, various properties, and finally stochastic integration leading to a brief survey of diffusion processes.

General Description of the Unit

This unit aims for an intuitive understanding of Brownian motion and stochastic calculus, although rigorous proofs will be presented for a few of the most beautiful results. Students should be comfortable with reading and understanding rigorous proofs. Understanding Brownian motion, commonly regarded as the canonical example of a martingale and a Markov process with continuous paths, is essential for any future study of stochastic processes and its applications.

Relation to Other Units

This unit is a first course in continuous time stochastic processes and introductory stochastic analysis.

## Intended learning outcomes

Learning Objectives

At the end of the unit students should:

• be able to recall all definitions and main results,
• be able to understand on an intuitive level the reasoning behind proofs of major results,
• be able to apply the theory in standard situations,
• be able to use the ideas of the unit in unseen situations

Transferable Skills

Understanding the behaviour of diffusion processes so as to be able to use them (e.g. perform calculations and write simulations) in problems arising in physics, engineering, financial calculus or statistics.

## Teaching details

Lectures supported by problem sheets and solution sheets.

## Assessment Details

80% Examination

20% Coursework

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.