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Hitting the blinking target under stochastic resetting.

Bartosz Żbik1, Bartłomiej Dybiec2, Karol Capała3,4

  • 1Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland.

Chaos (Woodbury, N.Y.)
|April 16, 2026
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Summary
This summary is machine-generated.

We derived formulas for first hitting times of stochastic processes with a switching target. Stochastic resetting was introduced, showing memory effects in the system dynamics.

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Area of Science:

  • Physics
  • Chemistry
  • Biology
  • Economics

Background:

  • First hitting times (FHTs) are crucial in modeling stochastic processes across scientific fields.
  • Standard FHT analysis assumes static targets, limiting applicability to dynamic systems.

Purpose of the Study:

  • To investigate FHT distributions for stochastic processes targeting a two-state switching (active/inactive) entity.
  • To analyze the impact of stochastic resetting on FHTs in this dynamic system.

Main Methods:

  • Derivation of closed-form analytical formulas for FHT distributions.
  • Integration of stochastic resetting into the underlying stochastic process.
  • Computer simulations using Langevin dynamics to validate analytical findings.

Main Results:

  • Closed-form solutions for FHT distributions with a switching target were obtained.
  • Formulas for FHTs under stochastic resetting were derived.
  • The study revealed that stochastic resetting introduces non-Markovian memory effects.

Conclusions:

  • The developed framework provides exact analytical solutions for FHTs in dynamic systems.
  • Stochastic resetting in this context leads to memory, complicating standard analysis.
  • The findings offer new tools for analyzing complex stochastic phenomena with dynamic targets.