Modelling events in time

Sections 1 and 2 introduce the fundamental ideas of random processes through a series of examples. Section 3 describes a model that is appropriate for events occurring ‘at random’ in such a way that their rate of occurrence remains constant. Section 4 derives the main results from Section 3. Section 5 introduces the multivariate Poisson process in which each event may be just one of several different types of event. Section 6 introduces the non-homogeneous Poisson process in which events occur at a rate that varies with time.

Course learning outcomes

After studying this course, you should be able to:

• Use the standard notation for random processes and identify the time domain and the state space of a random process
• Decide whether a process involving Bernoulli trials is a Bernoulli process
• Define the random variables X (t), X (t1, t2), Tn and Wn for a point process and use this notation when calculating probabilities associated with point processes
• Calculate probabilities associated with the Poisson process, the multivariate Poisson process and the non-homogeneous Poisson process
• Use relevant tables to simulate the occurrences of events in a Poisson process and in a non-homogeneous Poisson process.