Probability Seminar

SPEAKER: Prof. Kei Kobayashi, UTK

TITLE: SDEs driven by time-changed Levy processes and associated time-fractional

order Kolmogorov equations

ABSTRACT: It is known that if a stochastic process is a solution to a classical Ito SDE, then its transition probabilities satisfy in the weak sense the associated forward Kolmogorov or Fokker-Planck equation. In many applications, however, Kolmogorov-type equations with fractional derivatives in time are used to model anomalous subdiffusions. In this talk, we will see a class of time-fractional order or more general time-distributed order equations that are associated with SDEs driven by time-changed Levy processes, where the time-change is given respectively by the inverse of a single or mixture of independent stable subordinators.