A centra-limit theorem for conservative fragmentation chain

2022/10/14 by Noûs, Camille, Rubenthaler, Sylvain
#60F05 #60J80 #60K05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2210.07791

Abstract

We are interested in a fragmentation process. We observe fragments frozen when their sizes are less than ε (ε > 0). It is known ([BM05]) that the empirical measure of these fragments converges in law, under some renormalization. In [HK11], the authors show a bound for the rate of convergence. Here, we show a central-limit theorem, under some assumptions. This gives us an exact rate of convergence.

Related

• Central-limit theorem for conservative fragmentation chains
• Asymptotic properties of the process counted with a random characteristic in the context of fragmentation processes
• Strong Law of Large Numbers for Fragmentation Processes
• Limit theorems for fragmentation processes with immigration
• Martingales and Rates of Presence in Homogeneous Fragmentations