| Volume 15, Number 1, 2025, Pages - DOI：10.11948/JAAC-2023-0466 |
| Directed search process driven by Levy motion with stochastic resetting |
| Yan xu,Hexin Zhu |
| Keywords:stochastic resetting search processes renewal theory Levy process. |
| Abstract: |
| In this paper, We show how certain active transport processes in living cells
can be modeled in terms of a directed search process driven by Levy motion with stochastic
resetting. We consider the motor-driven intracellular transport of vesicles to synaptic
targets in the axons and dendrites of neurons, in this case, the restart duration of the
search process after reset is finite, which has two parts: a finite return time and a refractory
period. We use a probabilistic renewal method to calculate the splitting probabilities and
conditional mean first passage times (MFPTs) for capture by a finite array of contiguous
targets. We consider two different search scenarios: bounded search on the interval [0, L],
where L is the length of the array, with a refractory boundary at x = 0 and a reflecting
boundary at x = L (Model A), and partially bounded search on the half-line (Model B).
In the latter case there is a non-zero probability of can not to find a target in the absence
of resetting. We show that both models have the same splitting probabilities, and that
increasing the resetting rate r will lead to the splitting probability increases. On the
other hand the MFPTs for model A are monotonically increasing functions of r, whereas
the MFPTs of model B are non-monotonic respect to r, with a minimum at an optimal
resetting rate. |
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