DCU Home | Our Courses | Loop | Registry | Library | Search DCU


Module Specifications

Archived Version 2014 - 2015

Module Title
Module Code

Online Module Resources

NFQ level 8 Credit Rating 7.5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None

FIM3 version of Stochastic Modelling : This module provides a comprehensive introduction to Stochastic Processes and their applications. It does so by blending the development of the theory of Markov chains (both in disccrete and continuous time) with modelling examples . As a result , the module is of mixed "theory" and "know-how and skills" type .

Learning Outcomes

1. Construct Markov chain models for actuarial and financial processes.
2. Analyse any given chain in a systematic way , including determining its asymptotic behaviour.
3. Prove the main theorems governing Markov chains in discrete and continuous time.
4. State the definitions of the main concepts underlying the theory of Markov chains and demonstrate an understanding of these through examples and counter-examples.

Workload Full-time hours per semester
Type Hours Description
Lecture36No Description
Tutorial12No Description
Independent Study150No Description
Total Workload: 198

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Stochastic Modelling
Review of basic probabilistic concepts, the various types of stochastic processes, stationarity, Markov processes, the Chapman-Kolmogorov equation, stationary probability distributions. [CT4 - (ii)]

Markov Chains
Solution of the Chapman-Kolmogorov equation in matrix form, transition graph, finding the stationary distribution, actuarial examples; two-state chains; the limiting distribution of finite Markov chains, irreducibility and aperiodicity, exponential convergence; infinite Markov chains, criteria for recurrence, the limiting distribution and its relation to mean recurrence times; applications: queues, random walks with various boundary conditions. [CT4 - (iii)]

Markov Jump Processes
The infinitesimal generator, the forward and backward equations, solution in exponential form; holding times, exponential distribution, jump chain; the limiting distribution of a finite Markov jump process and its connection to mean recurrence times; the case of infinite state spaces, the integral form of the backward equation, the minimal process, conservative processes; the Poisson process and actuarial models; inhomogeneous Markov jump processes, time-dependent transition rates, the backward equation in differential and integral forms, residual holding times. [CT4 - (iv)]. Survival models, sickness and death, estimation of transition rates; finite population observed fora fixed time interval, truncated life-times, unbiased estimator of transition rate, asymptotic distribution, poisson approximation. [CT4 - (vii)]

Assessment Breakdown
Continuous Assessment% Examination Weight%
Course Work Breakdown
TypeDescription% of totalAssessment Date
Reassessment Requirement
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
Indicative Reading List

  • A.N. Other, Acted material for CT4 subject , models: 0,
  • Bhattacharya, R.N., and Waymire R.C: 1990, Stochastic Processes with Applications, Wiley, NewYork,
  • Grimmett, G.R. and Stirzaker, D.R. 1992, Probability and Random Processes, 2-nd Ed., Oxford UP Oxford: 0,
  • Norris, JR 1997, Markov Chains, Cambridge UP Cambridge: 0,
Other Resources

Programme or List of Programmes