MAT3206: Stochastic Processes

This course introduces stochastic processes starting with definitions of a stochastic process processes with stationary independent increments. The Poison process are singled out as a very useful and its properties are discussed with applications. Other processes considered are the birth, death and branching processes which are useful in disease modeling. The course winds up by considering the Markov chain: its definition, examples, transition probabilities and classification of the states and of chains. In all sections, real life applications are given.  Topics covered include: Poisson Processes; Birth and death processes; Branching Processes; and Markov chain. 

Course Objectives  
On successful completion of this course unit, the learners should be able to: 

• Define a stochastic process 
• State the properties of a Poison process 
• Apply Poison processes to real life situations 
• Estimate mean inter-arrival time and mean waiting time of events 
• Estimate the expected population size in a birth-death process 
• Solve differential equations using generating functions 
• Calculate the probability of extinction and the expected total population in a branching process 
• Classify states of Markov chain 
• Calculate mean first passage and recurrence times for an irreducible recurrent state Markov chain 
• Appreciate the range of applications and be able to model appropriate real-life problems in terms of a stochastic process 

Expected Learning Outcome
This course unit is meant: 

• To discuss the basic competence in the concepts, principle, procedures and application of single variable integral and differential calculus with continued emphasis on geometric interpretation and the use of a graphing calculator technology, when appropriate. 
• To encourage orderliness, speed and accuracy in the presentation of mathematics. 
• To help learners acquire the skills of expression in proper mathematical language and using mathematical symbols correctly. 
• To provide instruction that contributes to the learners’ abilities to think critically and solve real life problems, to reason mathematically and apply computational skills. 
• To build a strong foundation in calculus as preparation for subsequent courses in mathematics and other sciences.