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Abstract
Photon transport is considered in an interstellar cloud containing
one or several photon sources (stars), defined by
$q_i\delta( x- x_{\i})\,i=1,2,\ldots,$ where the
locations $x_i$'s are given in a stochastic way. First, the case
is examined of a single source of intensity $q_1$ and located at
$x_1$ with a probability density $p_1 = \p(x_1)$, such that
$\p(x_1)\geq 0$ and $\int_V \p(x_1)\dx_1 = 1$, where $V
\subset \R^3$ is the region occupied by the cloud. Then, a
Boltzmann-like equation for the average photon distribution function
< n >$(x,u;x_1)$ is derived and it is shown that
$\p(x_1)$ can be evaluated starting from a far-field measurement
of < n >. Finally, the case of two or more photon sources is
discussed: the corresponding results are reasonably simple if
$\p(x_1,x_2) = \p_1(x_1)\p_2(x_2)$, i.e. if the
locations of the two photon source are "independent".
Mathematics Subject Classification: 85A25, 35R30.
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