- Department: Mathematics
- Credit value: 10 credits
- Credit level: H
- Academic year of delivery: 2022-23
Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
Pre-requisites for Natural Sciences students: must have taken Statistics Option MAT00033I.
Occurrence | Teaching period |
---|---|
A | Autumn Term 2022-23 |
At the end of the module the student should be able to:
appreciate the uses for stochastic models, their characteristics and limitations;
explain the concept of continuous-time stochastic processes and the Markov property;
give examples of applications of stochastic processes;
formulate and analyse Markov models in continuous time;
calculate (conditional) probabilities of events and expectations of variables described by simple Markov processes like the Poisson process or the Wiener process;
determine transition rates stationary distributions of birth-death processes;
discuss the properties of the Wiener process;
define the Ito stochastic integral and give its important properties;
apply Ito's Lemma to find solutions of certain stochastic differential equations;
Principles of stochastic modelling
The need for models
Stochastic vs. deterministic models.
Continuous-time stochastic processes
The relevance of the Markov property
Discrete state-space: Markov jump processes
Poisson process
Birth-death processes
Kolmogorov equations (master equations)
Stationary distributions
Continuous state-space, stochastic calculus
Wiener process
Stochastic differential equations and Ito’s calculus. Examples include: geometric Brownian motion; Ornstein-Uhlenbeck process
Stochastic integration
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 100 |
None
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 100 |
Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
G R Grimmett & D R Stirzaker, Probability and random processes, OUP.
C W Gardiner, Handbook of stochastic methods, Springer.
T Mikosch, Elementary stochastic calculus with finance in view, World Scientific.
Z Brzezniak & T Zastawniak, Basic Stochastic Processes, Springer.