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The Fokker-Planck Equation and the First Exit Time Problem. A Fractional Second Order Approximation

  • Christos H. SkiadasEmail author
  • Charilaos Skiadas
Chapter

Abstract

We present a first exit time theory of a stochastic process. The general model is analytically derived according to the first exit time or hitting time theory for a stochastic process crossing a barrier. The derivation lines follow the transition probability densities from the Fokker-Planck equation. Then we find the probability density form and the first and second approximation of the first exit time densities. For the first approximation we obtain a generalization of the Inverse Gaussian whereas for the second approximation we apply a fractional approach to the second derivative by inserting a parameter k. We thus introduce another approach to apply a fractional theory.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.ManLab, Technical University of CreteChania, CreteGreece
  2. 2.Department of Mathematics and Computer ScienceHanover CollegeHanoverUSA

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