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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
Summary
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.
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.
