Multifractional Poisson process, multistable subordinator and related   limit theorems
  We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and establish the convergence of a continuous-time random walk to the multifractional Poisson process. 
Ilya Molchanov, Kostiantyn Ralchenko
math.PR