Stochastic Calculus

This module is a introduction to stochastic calculus. It begins with fundamental concepts in probability theory, stochastic processes, Brownian motion and martingales, leads on to stochastic integrals, chiefly Itô integrals and their properties, and Itô’s formulae, and finishes with a treatment of stochastic differential equations and a few applications in finance.

Course Information

Most modules require a 2.2 degree in a related discipline or equivalent professional experience. Should you have any queries regarding your eligibility, please contact us at

N.B. Required honours undergraduate degree (Level 8) a 2:1 (or equivalent grade) BSc in Financial Mathematics, Mathematics, Applied and Computational Mathematics, or Statistics.

The following topics will be covered:

  • Preliminaries - review of fundamental concepts, stochastic processes, Brownian motion, conditional expectation and martingales.
  • Stochastic Integrals - Riemann integrals and variants, Itô integrals and Itô formulae.
  • Multi-dimensional Itô Calculus - Definition of N-dimensional Itô process and properties, multi-dimensional Itô formulae; correlated Weiner processes.
  • Stochastic Differential Equations - review of deterministic ODEs, Itô SDEs and general linear SDEs.

Learn from world renowned academic staff in Ireland’s leading, future focused and globally recognised colleges.

Gain an accredited NFQ qualification/micro credential that you may count towards a full award if you so wish in the future.

Previous modules may be used as recognition of prior learning towards Advance Centre degree programmes.

Equip yourself with the latest in demand skillset, tools, know-how and knowledge to succeed in your career.

Gain a competitive edge, influence growth and steer strategic goals in your organisation upon completion of your studies with the Advance Centre.

Yes, if you complete this module it can be credited as part of the MSc Financial Mathematics Full Time or MSc Financial Mathematics Part Time.

Detailed Course Information

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