Practical Estimation and Simulation Analysis of the Kolmogorov Constant for Heavy-Tailed Noncritical Markov Branching Systems

Iskandarov  S.B; Asirov  J.J; Sobirov  U.M; Axmedov  Q.A

Authors

Iskandarov S.B Urgench State University named after Abu Rayhan Biruni
Asirov J.J Urgench State University named after Abu Rayhan Biruni
Sobirov U.M Urgench State University named after Abu Rayhan Biruni
Axmedov Q.A Urgench State University named after Abu Rayhan Biruni

Keywords:

Kolmogorov Constant, Heavy-Tailed Offspring Distribution, Monte Carlo Simulation, Continuous-Time Markov Branching Process, Survival Probability Asymptotics

Abstract

This paper presents a practical estimation and simulation-based study of the Kolmogorov constant in the context of heavy-tailed, noncritical continuoustime Markov branching systems. Building on the explicit analytic form recently derived for noncritical Markov branching models, we investigate the empirical behaviour of the survival probability and related asymptotic quantities under heavy-tailed offspring distributions using Monte Carlo simulation techniques.

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