Moments of Moments and Branching Random Walks

SOME RESULTS OF MOMENTS OF UNCERTAIN RANDOM VARIABLES

Chance theory is a mathematical methodology for dealing with indeterminatephenomena including uncertainty and randomness.Consequently, uncertain random variable is developed to describe the phenomena which involveuncertainty and randomness.Thus, uncertain random variable is a fundamental concept in chance theory.This paper provides some practical quantities to describe uncertain random variable...

Some Properties of Even Moments of Uniform Random Walks

We build upon previous work on the densities of uniform random walks in higher dimensions, exploring some properties of the even moments of these densities and extending a result about their modularity.

Harmonic continuous time branching moments

We show that the mean inverse populations of nondecreasing, square integrable, continuous-time branching processes decrease to zero like the inverse of their mean population if and only if the initial population k is greater than a first threshold m1 ≥ 1. If, furthermore, k is greater than a second threshold m2 ≥ m1, the normalized mean inverse population is at most 1/(k −m2). We express m1 and...

Branching Random Walks

We study a generalized branching random walk where particles breed at a rate which depends on the number of neighbouring particles. Under general assumptions on the breeding rates we prove the existence of a phase where the population survives without exploding. We construct a non trivial invariant measure for this case.

Branching Processes and Random Walks