Spectral expansion of the occupation measure for birth and death on a flow

A natural approach to investigating the dynamics of stochastic flows is to study the action of such flows on measures. In models of pollution transport the resulting measure-valued random process describes the distribution of pollutant mass in space. When, in addition, pollutants are allowed to ente...

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Bibliographic Details
Published in:Stochastic processes and their applications 1998-06, Vol.74 (2), p.203-215
Main Authors: Kao, John, Cinlar, Erhan
Format: Article
Language:English
Subjects:
Exact sciences and technology
Markov processes
Mass transport
Mathematics
Probability and statistics
Probability theory and stochastic processes
Random measures
Sciences and techniques of general use
Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)
Stochastic flows
Stochastic flows Random measures Mass transport
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Summary:A natural approach to investigating the dynamics of stochastic flows is to study the action of such flows on measures. In models of pollution transport the resulting measure-valued random process describes the distribution of pollutant mass in space. When, in addition, pollutants are allowed to enter and leave the space, the process is called “birth” and “death” on a flow. Here we study this model with an eye towards numerical calculation of its statistical descriptors (particularly the mean and covariance functionals). We propose a sequence of weak approximations convenient for numerics. This sequence is obtained by expanding a conditional mean measure in the eigenfunctions of a properly chosen self-adjoint operator.
ISSN:0304-4149
1879-209X
DOI:10.1016/S0304-4149(97)00110-5