Applications of Discrete-time Markov Chains and Poisson Processes to Air Pollution Modeling and Studies

In this brief we consider some stochastic models that may be used to study problems related toenvironmental matters, in particular, air pollution. The impact of exposure toair pollutants on people's health is a very clear and well documented subject. Therefore, it is veryimportant to obtain ways to predict or explain the behaviour of pollutants in general. Dependingon the type of question that one is interested in answering, there are several of ways studying thatproblem. Among them we may quote, analysis of the time series of the pollutants' measurements,analysis of the information obtained directly from the data, for instance, daily, weekly or monthlyaverages and standard deviations. Another way to study the behaviour of pollutants in general isthrough mathematical models. In the mathematical framework we may have for instance deterministic or stochastic models. The type of models that we are going to consider in this brief are thestochastic ones.