A general framework derives mean first passage times and moments for fixed-speed velocity jump processes in higher dimensions, yielding a universal MFPT form via two bias functions at low Knudsen numbers and anomalous scaling for narrow targets.
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For one-sided absorbing boundaries on the semi-infinite line, the first-passage time density scales as t to the power of -1/(2α)-1 at long times, with an optimal α minimizing the mean first-passage time.
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Mean first passage times of higher-dimensional velocity jump processes
A general framework derives mean first passage times and moments for fixed-speed velocity jump processes in higher dimensions, yielding a universal MFPT form via two bias functions at low Knudsen numbers and anomalous scaling for narrow targets.
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First-Passage Times for the Space-Fractional Spectral Fokker-Planck Equation
For one-sided absorbing boundaries on the semi-infinite line, the first-passage time density scales as t to the power of -1/(2α)-1 at long times, with an optimal α minimizing the mean first-passage time.