Fractional order Fokker-Planck-Kolmogorov equations and associated stochastic processes

  • Sabir Umarov
Part of the Developments in Mathematics book series (DEVM, volume 41)


This chapter discusses the connection between pseudo-differential and fractional order differential equations considered in Chapters 2–6 with some random (stochastic) processes defined by stochastic differential equations. We assume that the reader is familiar with basic notions of probability theory and stochastic processes, such as a random variable, its density function, mathematical expectation, characteristic function, etc. Since we are interested only in applications of fractional order ΨDOSS, we do not discuss in detail facts on random processes that are already established and presented in other sources. For details of such notations and related facts we refer the reader to the book by Applebaum [App09] (or [IW81, Sat99]). We only mention some basic notations directly related to our discussions on fractional Fokker-Planck-Kolmogorov equations.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Sabir Umarov
    • 1
  1. 1.Department of MathematicsUniversity of New HavenWest HavenUSA

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