The boundary non-Crossing probabilities for Slepian process

TL;DR

This paper derives explicit formulas for boundary non-crossing probabilities of Slepian processes with piecewise linear boundaries and develops approximations for general continuous boundaries, facilitating easier calculations.

Contribution

It provides the first explicit formula for boundary non-crossing probabilities of Slepian processes with piecewise linear boundaries and an approximation method for general continuous boundaries.

Findings

Explicit formula for piecewise linear boundaries

Approximation method for general continuous boundaries

Formulas are easy to implement computationally

Abstract

In this contribution we derive an explicit formula for the boundary non-crossing probabilities for Slepian processes associated with the piecewise linear boundary function. This formula is used to develop an approximation formula to the boundary non-crossing probabilities for general continuous boundaries. The formulas we developed are easy to implement in calculation the boundary non-crossing probabilities.