Asymptotic properties of fragmentation processes

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

The asymptotic behavior of fragmentation processes

The fragmentation processes considered in this work are self-similar Markov processes which are meant to describe the ranked sequence of the masses of the pieces of an object that falls apart randomly as time passes. We investigate their behavior as t → ∞. Roughly, we show that the rate of decay of the ℓ p-norm (where p > 1) is exponential when the index of self-similarity α is 0, polynomial wh...

2 Asymptotic formula for a partition function of reversible coagulation - fragmentation processes

We construct a probability model seemingly unrelated to the considered stochastic process of coagulation and fragmentation. By proving for this model the local limit theorem, we establish the asymptotic formula for the partition function of the equilibrium measure for a wide class of parameter functions of the process. This formula proves the conjecture stated in [5] for the above class of proc...

Asymptotic behavior of solutions to the fragmentation equation with shattering: an approach via self-similar Markov processes

The subject of this paper is a fragmentation equation with non-conservative solutions, some mass being lost to a dust of zero-mass particles as a consequence of an intensive splitting. Under some assumptions of regular variation on the fragmentation rate, we describe the largetime behavior of solutions. Our approach is based on probabilistic tools: the solutions to the fragmentation equation ar...

Asymptotic properties of the sample mean in adaptive sequential sampling with multiple selection criteria

‎We extend the method of adaptive two-stage sequential sampling to‎‎include designs where there is more than one criteria is used in‎‎deciding on the allocation of additional sampling effort‎. ‎These‎‎criteria‎, ‎or conditions‎, ‎can be a measure of the target‎‎population‎, ‎or a measure of some related population‎. ‎We develop‎‎Murthy estimator for the design that is unbiased estimators for‎‎t...

Stochastic Coagulation-fragmentation Processes with a Finite Number of Particles and Applications

Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention especially in stochastic analysis and statistical physics of cellular biology, as novel experimental data are now available, but their interpretation remains challen...