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Estimation of Weak Lensing Parameters by Stochastic Integration

by W. P. Petersen

(Report number 2000-06)

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.

Keywords: cosmology: theory, gravitational lensing,distance scale, methods: numerical, statistical

@Techreport{P00_265,
  author = {W. P. Petersen},
  title = {Estimation of Weak Lensing Parameters by Stochastic Integration},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2000-06},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2000/2000-06.pdf },
  year = {2000}
}

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