grandes-ecoles 2015 QV.D.2

grandes-ecoles · France · centrale-maths1__psi Probability Definitions Almost Sure Convergence and Measure-Theoretic Probability

We assume $m>1$. We study the Galton-Watson process with $Y_n$ the number of individuals in generation $n$ (starting from 1 individual).
Show that the probability that the sequence $(Y_n)_{n\in\mathbb{N}^*}$ takes any fixed value $k$ infinitely many times is zero.

We assume $m>1$. We study the Galton-Watson process with $Y_n$ the number of individuals in generation $n$ (starting from 1 individual).

Show that the probability that the sequence $(Y_n)_{n\in\mathbb{N}^*}$ takes any fixed value $k$ infinitely many times is zero.

Paper Questions

QI.A.1 QI.A.2 QI.A.3 QI.B QI.C QI.D.1 QI.D.2 QI.E.1 QI.E.2 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.A.5 QII.B QII.C.1 QII.C.2 QIII.A.1 QIII.A.2 QIII.A.3 QIII.A.4 QIII.B.1 QIII.B.2 QIII.C.1 QIII.C.2 QIII.C.3 QIV.A QIV.B QIV.C QIV.D QIV.E QIV.F QIV.G QV.A QV.B.1 QV.B.2 QV.C.1 QV.C.2 QV.D.1 QV.D.2 QV.E QV.F