Evolution of the probability distribution function of galaxies in redshiftspace

We present a new analytic calculation for the redshift-space evolution of t he one-point galaxy probability distribution function (PDF). The non-linear evolution of the matter density field is treated by second-order Eulerian perturbation theory and transformed to the galaxy density field via a secon d-order local biasing scheme. We then transform the galaxy density field to redshift space, again to second order. Our method uses an exact statistica l treatment based on the Chapman-Kolmogorov equation to propagate the proba bility distribution of the initial mass field to the final redshifted galax y density field. The moment generating function of the PDF is derived and u sed to find a new, closed-form expression for the skewness of the redshifte d galaxy distribution. The formalism is shown to be general enough to allow a non-deterministic (or stochastic) biasing prescription. We demonstrate t he dependence of the redshift-space PDF on cosmological and biasing paramet ers. Our results are compared with existing models for the PDF in redshift space and with the results of biased N-body simulations. We find that our P DF accurately models the redshift-space evolution and the non-linear biasin g.