First-hitting-time model

Quantum mechanics

Statistics

Hitting time

Brownian motion

Stochastic process

Applied mathematics

Set (abstract data type)

Computer science

Classical mechanics

Statistical physics

Geology

Oceanography

Physics

Mathematics

Mathematical analysis

Particle (ecology)

Interval (graph theory)

Combinatorics

Programming language

Mechanics

Physical review. E

We consider a Brownian particle diffusing in a one-dimensional interval with absorbing end points. We study the ramifications when such motion is interrupted and restarted from the same initial configuration. We provide a comprehensive study of the first-passage properties of this trapping phenomena. We compute the mean first-passage time and derive the criterion on which restart always expedites the underlying completion. We show how this set-up is a manifestation of a success-failure problem. We obtain the success and failure rates and relate them with the splitting probabilities, namely the probability that the particle will eventually be trapped on either of the boundaries without hitting the other one. Numerical studies are presented to support our analytic results.

First passage under stochastic resetting in an interval