MA4APS: Applied Stochastic Processes

Module code: MA4APS

Module provider: Mathematics and Statistics; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: 7

When you’ll be taught: Semester 1

Module convenor: Dr Abhishek Pal Majumder , email: a.palmajumder@reading.ac.uk

Module co-convenor: Dr Patrick Ilg, email: p.ilg@reading.ac.uk

Pre-requisite module(s): BEFORE TAKING THIS MODULE YOU MUST TAKE MA2DE AND TAKE ST1PS (Compulsory)

Co-requisite module(s):

Pre-requisite or Co-requisite module(s):

Module(s) excluded: IN TAKING THIS MODULE YOU CANNOT TAKE MA3APS OR TAKE MA3AST (Compulsory)

Placement information: NA

Academic year: 2025/6

Available to visiting students: Yes

Talis reading list: Yes

Last updated: 29 April 2025

Overview

Module aims and purpose

To introduce the concept of stochastic processes and to enable students to solve problems involving stochastic processes from a variety of applications like molecular motion, population dynamics, weather, and finances. 

Module learning outcomes

By the end of the module, it is expected that students will be able to:

1. Formulate, solve, and critically analyse discrete stochastic processes using Markov chains with some rigour;
2. Demonstrate a comprehensive understanding of continuous time Markov chains to evaluate critically queuing models with a variety of practical applications;
3. Systematically understand stochastic integrals and stochastic differential equations;
4. Apply the above concepts to solve current problems from a wide variety of fields from physics to finances and evaluate the applicability of the models.

Module content

• Discrete Markov chains, limit theorems, applications to population dynamics; 
• Continuous time Markov chains such as queuing models; 
• Markov processes, Wiener process, methods for solution of diffusion equation, examples from molecular motion and economics; 
• Stochastic integrals, stochastic differential equations, their properties and methods of solution. Applications to Brownian motion and stock market. 

Structure

Teaching and learning methods

Lectures supported by problem sheets and tutorials. 

Study hours

At least 54 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.