An extension of a functional equation of Poincaré and Mandelbrot
An extension of a functional equation of Poincaré and Mandelbrot
We consider the distributional equation Z -A\Z\ + ... 4-A^Z^, where iV, Ai, Z, Zi are independent real random variables with N 6 N and Ai > 0. Each Ai is equally distributed as Ai and each Zi as Z; the distribution of Z is unknown.After establishing theorems about existence …