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...

Under proper scaling and distributional assumptions, we prove the convergence in the Skorokhod space endowed with the M1-topology of a sequence of stochastic integrals of a deterministic function driven by a time-changed symmetric α-stable Lévy process. The time change is given by the inverse...

Fractional Poisson processes, a rapidly growing area of non-Markovian stochastic processes, are useful in statistics to describe data from counting processes when waiting times are not exponentially distributed. We show that the fractional Kolmogorov–Feller equations for the probabilities at...