Blog
About

  • Record: found
  • Abstract: found
  • Article: found
Is Open Access

SDEs driven by a time-changed L\'evy process and their associated time-fractional order pseudo-differential equations

Preprint

Read this article at

Bookmark
      There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

      Abstract

      It is known that the transition probabilities of a solution to a classical It\^o stochastic differential equation (SDE) satisfy in the weak sense the associated Kolmogorov equation. The Kolmogorov equation is a partial differential equation with coeffcients determined by the corresponding SDE. Time-fractional Kolmogorov type equations are used to model complex processes in many fields. However, the class of SDEs that is associated with these equations is unknown except in a few special cases. The present paper shows that in the cases of either time-fractional order or more general time-distributed order differential equations, the associated class of SDEs can be described within the framework of SDEs driven by semimartingales. These semimartingales are time-changed L\'evy processes where the independent time-change is given respectively by the inverse of a single or mixture of independent stable subordinators. Examples are provided, including a fractional analogue of the Feynman-Kac formula.

      Related collections

      Most cited references 10

      • Record: found
      • Abstract: not found
      • Article: not found

      The random walk's guide to anomalous diffusion: a fractional dynamics approach

        Bookmark
        • Record: found
        • Abstract: not found
        • Article: not found

        Random Walks on Lattices. II

          Bookmark
          • Record: found
          • Abstract: found
          • Article: not found

          Single-particle tracking: applications to membrane dynamics.

          Measurements of trajectories of individual proteins or lipids in the plasma membrane of cells show a variety of types of motion. Brownian motion is observed, but many of the particles undergo non-Brownian motion, including directed motion, confined motion, and anomalous diffusion. The variety of motion leads to significant effects on the kinetics of reactions among membrane-bound species and requires a revision of existing views of membrane structure and dynamics.
            Bookmark

            Author and article information

            Journal
            0907.0253
            10.1007/s10959-010-0289-4
            ScienceOpen disciplines:

            Comments

            Comment on this article