Expediting Feller process with stochastic resetting

Area of Science:

• Statistical Physics
• Stochastic Processes
• Mathematical Biology

Background:

• The Feller process models diffusion with space-dependent coefficients and a confining potential, applicable to biological and social phenomena where negative values are impossible.
• Stochastic resetting introduces random re-initializations to a diffusion process, altering its first-passage time properties.

Purpose of the Study:

• To investigate the impact of Poissonian stochastic resetting on the first-passage properties of the Feller diffusion process.
• To derive exact expressions for the mean first-passage time under resetting and identify conditions for accelerated first-passage.

Main Methods:

• Utilized the Fokker-Planck equation to describe the Feller diffusion process with stochastic resetting.
• Derived closed-form expressions for the Laplace transform of the survival probability.
• Analyzed the optimal resetting rate and maximal speedup to determine phase spaces where resetting is beneficial.

Main Results:

• Obtained exact expressions for the mean first-passage time (⟨T_r⟩) with Poissonian resetting.
• Identified critical values (θ_c) determining the efficacy of resetting based on initial (x_0) and absorbing boundary (x_a) positions.
• Found that for x_0 < x_a, resetting accelerates first-passage for θ < θ_c, while for x_a < x_0, acceleration occurs for θ > θ_c.

Conclusions:

• Poissonian resetting can significantly accelerate first-passage times in Feller diffusion, but its effectiveness is highly dependent on the system's parameters.
• The study elucidates the phase space where resetting provides a speedup, offering insights for optimizing processes in relevant scientific fields.
• This work provides a foundation for exploring resetting in more complex, case-specific Feller diffusion models.