Stochastic Processes

Objectives

Main goals

Being a course for the third year of the degree in Mathematics of FCT/UNL, in the branch Applied Mathematics, this course intends to give appropriate knowledge foundations for the study of the evolution of random phenomena.

-Main goals related to knowledge:
Knowledge of some essential notions for the understanding of stochastic processes such as Kolmogorov''''''''''''''''s conditional expectation. Knowledge of some of the fundamental examples of discrete and continuous time stochastic processes, their main properties and examples of relevant applications.

- Main goals related to know-how:
-generic:
To acknowledge and make use of the main properties of chosen examples of stochastic processes in discrete and continuous time pertinent for applications. To be able to decide which is the more appropriate model of a stochastic process to use when faced with a realistic situation.
-specific:
To master conditional expectation properties and methods of calculation. To identify a martingale and utilize the characteristic properties of this type of processes in the study of its behaviour, in particular, in the determination of a possible asymptotic behaviour. To identify a Markov chain and utilize the characteristic properties of this type of processes for the analysis of a concrete model. Identical set of competencies for Poisson and Wiener processes.