Sign changes as a universal concept in first-passage-time calculations.

Area of Science:

• Physics
• Mathematics
• Computational Science

Background:

• First-passage-time problems are crucial in diverse scientific fields.
• Existing analytical methods often require strict conditions, limiting their application.
• Numerical computations are frequently used due to the complexity of these problems.

Purpose of the Study:

• To develop a generalized analytical approach for first-passage-time distributions.
• To address the challenges associated with nondifferentiable Gaussian processes.
• To provide a more accessible method for first-passage-time calculations.

Main Methods:

• Developed a novel analytical framework for first-passage-time problems.
• Utilized the concept of sign changes to generalize first-passage event detection.
• Applied the method to nondifferentiable Gaussian processes.

Main Results:

• Successfully derived first-passage-time distributions for a wide class of nondifferentiable Gaussian processes.
• Demonstrated the effectiveness of the sign change concept for identifying first-passage events.
• Showcased the method's robustness across varying time-dependent boundaries and noise levels.

Conclusions:

• The presented analytical approach simplifies first-passage-time calculations for complex processes.
• This method overcomes common computational hurdles, enhancing research in related fields.
• Offers a powerful tool for analyzing transport phenomena, evolutionary dynamics, and more.