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Scaled Brownian motion with renewal resetting.

Anna S Bodrova1,2,3, Aleksei V Chechkin4,5, Igor M Sokolov1

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This study explores renewal processes with intermittent scaled Brownian motion. Erasing memory of the diffusion coefficient significantly alters probability densities and search efficiency.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Stochastic Processes

Background:

  • Investigates intermittent stochastic processes with time-dependent diffusion coefficients.
  • Focuses on scaled Brownian motion (SBM) with stochastic resetting.
  • Considers renewal processes where diffusion coefficient memory is erased upon resetting.

Purpose of the Study:

  • Analyze the impact of erasing diffusion coefficient memory in renewal SBM processes.
  • Compare properties of probability densities with and without memory retention.
  • Examine first-passage properties and search efficiency in renewal SBM.

Main Methods:

  • Mathematical modeling of stochastic processes.
  • Analysis of probability densities for renewal processes.
  • Investigation of first-passage time statistics.

Main Results:

  • Demonstrates vastly different probability density properties when diffusion coefficient memory is erased versus retained.
  • Characterizes the first-passage properties of scaled Brownian motion with renewal resetting.
  • Identifies the dependence of search efficiency on process parameters.

Conclusions:

  • Renewal processes with erased diffusion coefficient memory exhibit distinct behaviors compared to those retaining memory.
  • The study provides insights into the dynamics and efficiency of search strategies in complex stochastic systems.