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## Über dieses Buch

​In this brief we consider some stochastic models that may be used to study problems related to environmental matters, in particular, air pollution. The impact of exposure to air pollutants on people's health is a very clear and well documented subject. Therefore, it is very important to obtain ways to predict or explain the behaviour of pollutants in general. Depending on the type of question that one is interested in answering, there are several of ways studying that problem. 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 monthly averages and standard deviations. Another way to study the behaviour of pollutants in general is through 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 the stochastic ones.​

## Inhaltsverzeichnis

### Chapter 1. Introduction

Abstract
In this chapter we present a brief introduction to Markov chain theory, Bayesian statistics, and Markov chain Monte Carlo methods. We also present a description of the types of problems that will be analyzed using Markov chain methods and Poisson models.
Eliane Regina Rodrigues, Jorge Alberto Achcar

### Chapter 2. Markov Chain Models

Abstract
In this chapter some Markov chain models are presented together with some of their applications to air pollution problems. One of the questions answered is related to the probability of having a pollutant’s concentration between two thresholds of interest. A particular case of this problem is related to the probability of surpassing or not surpassing environmental standards.
Eliane Regina Rodrigues, Jorge Alberto Achcar

### Chapter 3. Poisson Models and Their Application to Ozone Data

Abstract
In this chapter we consider some Poisson models (homogeneous and non-homogeneous) to study the number of times a surpassing of a environmental threshold occurs within a time interval of interest. The results are applied to ozone data from the monitoring network of Mexico City.
Eliane Regina Rodrigues, Jorge Alberto Achcar

### Chapter 4. Modeling the Time Between Ozone Exceedances

Abstract
In this chapter we present some models to study the time between two exceedances of a given environmental threshold. The models are related to the Poisson processes formulation. However, the hon-homogeneity is captured by using different rate functions for different splitting of the observational period.
Eliane Regina Rodrigues, Jorge Alberto Achcar

### Chapter 5. Some Counting Processes and Ozone Air Pollution

Abstract
In this chapter we consider some counting processes more general than the Poisson process to study the distribution of the time between surpassings of a given environmental standard.
Eliane Regina Rodrigues, Jorge Alberto Achcar