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Stochastic models of environmental pollution

Part of: Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  01 July 2016

G. Kallianpur  and
J. Xiong
G. Kallianpur
Affiliation:
University of North Carolina at Chapel Hill
J. Xiong*
Affiliation:
University of North Carolina at Chapel Hill
*
* Postal address: Department of Statistics, Phillips Hall, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3260.
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Abstract

In this paper, we consider several stochastic models arising from environmental problems. First, we study pollution in a domain where undesired chemicals are deposited at random times and locations according to Poisson streams. The chemical concentration can be modeled by a linear stochastic partial differential equation (SPDE) which is solved by applying a general result. Various properties, especially the limit behavior of the pollution process, are discussed. Secondly, we consider the pollution problem when a tolerance level is imposed. The chemical concentration can still be modeled by a SPDE which is no longer linear. Its properties are investigated in this paper. When the leakage rate is positive, it is shown that the pollution process has an equilibrium state given by the deterministic model treated in [2]. Finally, the linear filtering problem is considered based on the data of several observation stations.

Keywords

POLLUTION PROCESSSTOCHASTIC PARTIAL DIFFERENTIAL EQUATIONPOISSON RANDOM MEASURELINEAR FILTERING

MSC classification

Primary: 60G55: Point processes
Secondary: 60H15: Stochastic partial differential equations
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 2 , June 1994 , pp. 377 - 403
Copyright
Copyright © Applied Probability Trust 1994 

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References

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