First exit time of a Lévy flight from a bounded region in ℝN

What is it about?

A Levy flight is a class of random walks that is characterized by a heavy-tailed step-length distribution. This work analyzes how long it takes to escape a given bounded region (called the first exit time) when an object moves according to a Levy flight.

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Why is it important?

We present tight upper and lower bounds on the tail distribution of the first exit time, and provide the exact asymptotics of the mean first exit time for a given range of step-length distribution parameters.