Stochastic radiative transfer in Markovian mixtures: Past, present, and future

The Markovian approach, originally suggested in the early 1900s, has widespread practical use in many of our present-day studies and allows one to build bridges between diverse research areas such as statistical physics, astronomy, and computational science. This overview takes a broad sweep of several important examples with the emphasis on the stochastic radiative transfer in a cloudy atmosphere. In particular, the overview (i) highlights important contributions made by Pomraning and Titov to the neutron and radiation transport theory in a stochastic medium with homogeneous statistics and (ii) illustrates that ideas and tools introduced by these two distinguished scientists are gaining increasing impact and recognition in the atmospheric science. (C) 2010 Elsevier Ltd. All rights reserved.