Milne's equation for polarized light and a related Markov process

Abstract

Starting from the radiative transfer equation for polarized light formulated with the help of the intensity tensor we introduce the mean intensity tensor. We derive the analogue of Milne's integral equation and interpret that equation as the potential equation of a Markov process.

Keywords:

• theoretical astrophysics
• radiative transfer
• discrete time Markov processes
• probabilistic potential theory
• noncommutative probabilities

AMS 2000 Subject Classification:

• Primary: 85A25
• Secondary: 60J05, 60J45, 46L53