Renewal analysis for higher moments in stochastic transport.

Details Renewal analysis for higher moments in stochastic transport. Renewal analysis for higher moments in stochastic transport.

Mar 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997jqsrt..57..295p&link_type=abstract

Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 57, issue 3, pp. 295-307

Statistics

1

Radiative Transfer: Numerical Methods

Scientific paper

This paper considers steady-state particle transport and radiative transfer through a stochastic mixture consisting of two immiscible materials. The statistics of the mixing of the two components of the medium are allowed to be very general; in particular, they are not necessarily Markovian. In the absence of scattering, the theory of alternating renewal processes is used to obtain an exact set of integral equations describing the ensemble average of any integer power of the stochastic intensity field. These equations are solved in an infinite medium with homogeneous statistics, and this solution is used to develop a simpler, but approximate, formalism for treating particle transport in a non-Markovian mixture. This simplified description is in the form of differential, rather than integral, equations, and results from a modification of the differential Markovian equations which arise from the use of the stochastic Liouville master equation.

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