Symmetry of Markov Random Evolutionary Processes in R n
Dmitri Koroliouk, Igor Samoilenko · 2023
This chapter introduces into R n the notion of symmetrization of a random vector, which generalizes the concept of symmetrization of a random variable and has interesting group properties. It aims to prove the symmetry of the Markov random evolutionary process. Symmetrical distributions play a significant role in probability theory and mathematical statistics. In particular, the chapter mentions the triangular distribution, the double exponential distribution and the Bessel distribution. Random variables with such distributions are symmetrical due to the fact that they can be written as the difference of two independent identically distributed random variables. The chapter deals with n independent identically distributed random variables.