Boundary crossing probabilities for diffusions with piecewise linear drifts

2012/05/14 by Jinghai Shao, Shao, Jinghai, Liqun Wang +1
Decision Sciences · Engineering · Mathematics · #60J65 #60J70 (Secondary) #60J75 (Primary) 60J60 #FOS: Mathematics #Probabilistic and Robust Engineering Design #Probability (math.PR) #Reliability and Maintenance Optimization #Statistical Distribution Estimation and Applications #math.PR #msc:60J60 #msc:60J65 #msc:60J70 #msc:60J75

paper · pdf · doi:10.48550/arxiv.1205.2941

openalex publication_date 2012/05/14 · arxiv created 2015/10/27 · arxiv updated 2015/10/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We propose an approach to approximate the boundary crossing probabilities for general one-dimensional diffusion processes, and derive the convergence rate for this approximation scheme. There results are based on the explicit expression of the Laplace transforms of the first passage densities for diffusions with piecewise linear drifts. The proposed method is applied to a reliability problem where the standard degradation model based on Wiener process is extended to diffusion processes with piecewise linear drifts.

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