Estimation of Weak Lensing Parameters by Stochastic Integration

Abstract

A procedure for computing distance-redshift statistics in inhomogeneous universes is described. Interpreting the generalizedDyer-Roeder equation as a stochastic differential equation permits a treatment of the shearing forces as Brownian movementand yields a straightforward Monte-Carlo simulation. Shear distributions taken from N-body simulations give a redshift dependent diffusion coefficient which is used toproduce a $C^{0}$ analytical model approximating the Weyl term in Sachs' equations.