Time-Non-Local Pearson Diffusions

Abstract In this paper we focus on strong solutions of some heat-like problems with a non-local derivative in time induced by Bernstein function and an elliptic operator given the generator or Fokker–Planck Pearson diffusion, covering large class important stochastic processes. Such kind time-non-local equations naturally arise treatment particle motion heterogeneous media. particular, use spectral decomposition results for usual diffusions to exploit explicit aforementioned equations. Moreover, provide representation such terms time-changed diffusions. Finally, further properties these processes, as limit distributions long/short-range dependence.