Application of a Stochastic Model to Environmental Pollution

Environmental pollution can afflict humans and plants with varying degree of discomfort, allergies, and even death. It may also harm the built environment and the natural environment. In this work, we considered pollution caused by air and noise using data from Oyo State Ministry of Environment in Ibadan, Nigeria. In describing the random characteristics of the data obtained, this study used discrete-time Markov chain (DMC). Markov chain with multiple states were used to represent the various levels of noise pollution and air quality. The limiting distribution for every pollution state were determined and it was concluded that the Markov chain is an ergodic Markov chain. The mean return time and the limiting distribution both indicated that there is little chance of unfavourable events occurring. Therefore, the standard of air and noise quality in the study area is thought to be in the range that is healthy.