On the expected moments between two identical random processes with application to sensor network

Abstract

We give a closed analytical formula for expected distance to the power $a$ between two identical general random processes, when $a$ is an even positive number. As an application to sensor network we prove that the optimal transportation cost to the power $b>0$ of the maximal random bicolored matching with edges $\{X_k,Y_k\}$ is in $\frac{\Theta \left(n^{\frac{b}{2}+1}\right)}{{\lambda }^b}$ when $b\ge 2,$ and in $\frac{O\left(n^{\frac{b}{2}+1}\right)}{{\lambda }^b}$ when $0<b<2.$

References in corpus (1)

• On the moment distance of Poisson processes