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Telegraphic processes with stochastic resetting.

Jaume Masoliver1

  • 1Department of Condensed Matter Physics and Institute of Complex Systems (UBICS), University of Barcelona, Catalonia, Spain.

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Summary
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Random resetting stabilizes telegrapher

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Area of Science:

  • Physics
  • Stochastic Processes
  • Mathematical Modeling

Background:

  • Diffusion processes assume instantaneous signal propagation.
  • Telegrapher's processes model finite signal propagation speed.
  • Resetting mechanisms alter random process dynamics.

Purpose of the Study:

  • Investigate resetting effects on telegrapher's processes.
  • Analyze consequences of finite signal propagation speed.
  • Compare resetting in telegraphic vs. diffusion processes.

Main Methods:

  • Mathematical analysis of stochastic processes.
  • Derivation of evolution equations for probability density.
  • Study of limiting cases for telegrapher's processes with resetting.

Main Results:

  • Random resetting stabilizes telegrapher's processes around the reset position.
  • Resetting optimizes the mean first-arrival time in telegraphic processes.
  • Exact evolution equations for the probability density were obtained.

Conclusions:

  • Finite signal propagation speed does not prevent stabilization by resetting.
  • Random resetting is a versatile mechanism for controlling stochastic processes.
  • Findings extend understanding of anomalous diffusion and transport phenomena.