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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Skiadas, C.H., Skiadas, C. (2018). The Fokker-Planck Equation and the First Exit Time Problem. A Fractional Second Order Approximation. In: Skiadas, C. (eds) Fractional Dynamics, Anomalous Transport and Plasma Science. Springer, Cham. https://doi.org/10.1007/978-3-030-04483-1_3
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DOI: https://doi.org/10.1007/978-3-030-04483-1_3
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