Occupancy Schemes Associated to Yule Processes
نویسندگان
چکیده
An occupancy problem with an infinite number of bins and a random probability vector for the locations of the balls is considered. The respective sizes of bins are related to the split times of a Yule process. The asymptotic behavior of the landscape of first empty bins, i.e., the set of corresponding indices represented by point processes, is analyzed and convergences in distribution to mixed Poisson processes are established. Additionally, the influence of the random environment, the random probability vector, is analyzed. It is represented by two main components: an i.i.d. sequence and a fixed random variable. Each of these components has a specific impact on the qualitative behavior of the stochastic model. It is shown in particular that for some values of the parameters, some rare events, which are identified, play an important role on average values of the number of empty bins in some regions.
منابع مشابه
Dual random fragmentation and coagulation and an application to the genealogy of Yule processes
The purpose of this work is to describe a duality between a fragmentation associated to certain Dirichlet distributions and a natural random coagulation. The dual fragmentation and coalescent chains arising in this setting appear in the description of the genealogy of Yule processes.
متن کاملFrom infinite urn schemes to decompositions of self-similar Gaussian processes
We investigate a special case of infinite urn schemes first considered by Karlin (1967), especially its occupancy and odd-occupancy processes. We first propose a natural randomization of these two processes and their decompositions. We then establish functional central limit theorems, showing that each randomized process and its components converge jointly to a decomposition of a certain self-s...
متن کاملThree efficient algorithms for implementing the preferential attachment mechanism in Yule-Simon Stochastic Process
We describe how different optimized algorithms may be effective in implementing the preferential attachment mechanism in different cases. We analyze performances with respect to different values of some parameters related to the Yule process associated to the preferential attachment. We examine how performance scales with system size and provide extensive simulations to support our theoretical ...
متن کاملA Yule - Simon process with memory
– The Yule-Simon model has been used as a tool to describe the growth of diverse systems, acquiring a paradigmatic character in many fields of research. Here we study a modified Yule-Simon model that takes into account the full history of the system by means of an hyperbolic memory kernel. We show how the memory kernel changes the properties of preferential attachment and provide an approximate...
متن کاملMonitoring the censored lognormal reliability data in a three-stage process using AFT model
Improving the product reliability is the main concern in both manufacturing and service processes which is obtained by monitoring the reliability-related quality characteristics. Nowadays, products or services are the result of processes with dependent stages referred to as multistage processes. In these processes, the quality characteristic in each stage is affected by the quality characterist...
متن کامل