Keywords
double diffusivity
first-passage time
Fokker-Planck Equation
Brownian motion
How to Cite
Abstract
The concept of stochastic resetting emerged in 2011, introducing a simple modification to [15] the one-dimensional Random Walk that leads to a stationary distribution and where the first-passage time can be easily optimized. In this context, we will investigate what happens when modeling these phenomena in a framework where a Brownian particle alternates between different states. We will derive the Fokker-Planck equations of the model and analyze the behavior of the probability density of the particle positions for long times and solve the corresponding first-passage time problem. Contrasting with the two-state Brownian motion, we will observe how resetting ensures a stationary behavior in the long run leading to a finite expectation for the first-passage problem. Finally, we will demonstrate how the existence of this expectation guarantees minimum values by varying the resetting or state-change parameters.
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