Approximation of the number of descendants in branching processes

Abstract

We discuss approximations of the relative limit densities of descendants in Galton--Watson processes that follow from the Karlin--McGregor near-constancy phenomena. These approximations are based on the fast exponentially decaying Fourier coefficients of Karlin--McGregor functions and the binomial coefficients. The approximations are sufficiently simple and show good agreement between approximate and exact values, which is demonstrated by several numerical examples.

I found how to improve the $\Gamma$-approximation. The good binomial approximations remain unchanged

References in corpus (2)

• Oscillatory critical amplitudes in hierarchical models and the tail of the Harris random variable
• Exponential stochastic compression of one-dimensional space and 146 percent