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Fractional Differential Equations Arising from Stochastic Dynamical Systems

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FDE2 - Fractional differential equations

Complex dynamical systems are often under random fluctuations. The noisy fluctuations may be Gaussian or non-Gaussian, which are usually modeled by Brownian motion or α-stable Levy motion, respectively.  Stochastic differential equations are appropriate mathematical models for these systems. At a certain ‘macroscopic’ level, non-Gaussianity of the noise manifests as a fractional or nonlocal operator, which facilitates the investigation of stochastic dynamical behaviours.  The speaker will overview recent advances in deterministic methods for non-Gaussian stochastic dynamical systems, including mean exit time, escape probability, and most probable transition pathways.  These methods involve fractional/nonlocal differential equations with singular integral operators.

This talk is part of the Isaac Newton Institute Seminar Series series.

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