2014•arXiv (Cornell University)Open access

Multifractional Poisson process, multistable subordinator and related\n limit theorems

Ilya Molchanov, Kostiantyn Ralchenko

Abstract

We introduce a multistable subordinator, which generalizes the stable\nsubordinator to the case of time-varying stability index. This enables us to\ndefine a multifractional Poisson process. We study properties of these\nprocesses and establish the convergence of a continuous-time random walk to the\nmultifractional Poisson process.\n

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Key concepts: Subordinator, Poisson distribution, Limit (mathematics), Stability (learning theory), Convergence (economics), Mathematics, Compound Poisson process, Process (computing)