  The propagation of light in a scattering medium is described as the motion of
a special kind of a Brownian particle on which the fluctuating forces act only
perpendicular to its velocity. This enforces strictly and dynamically the
constraint of constant speed of the photon in the medium. A Fokker-Planck
equation is derived for the probability distribution in the phase space
assuming the transverse fluctuating force to be a white noise. Analytic
expressions for the moments of the displacement $<x^{n}>$ along with an
approximate expression for the marginal probability distribution function
$P(x,t)$ are obtained. Exact numerical solutions for the phase space
probability distribution for various geometries are presented. The results show
that the velocity distribution randomizes in a time of about eight times the
mean free time ($8t^*$) only after which the diffusion approximation becomes
valid. This factor of eight is a well known experimental fact. A persistence
exponent of $0.435 \pm 0.005$ is calculated for this process in two dimensions
by studying the survival probability of the particle in a semi-infinite medium.
The case of a stochastic amplifying medium is also discussed.
