The course introduces students to stochastic processes starting with definitions of a stochastic process, processes with stationary and independent increments. The Poisson process is singled out as a very useful process and its properties are discussed with applications. Other processes considered are the birth, death and branching processes that are useful in disease modelling. 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.
By the end of this course students should be able to:· Define a stochastic process.· State the properties of a Poisson process.· Apply Poisson 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 difference equations using generating functions.· Calculate the probability of extinction and the expected total population in a branching process.· Classify states of a 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.
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