Distribution function of the blow up time of the solution of an\n anticipating random fatigue equation

2019/09/19 by Liliana Peralta, Peralta, Liliana
Decision Sciences · #FOS: Mathematics #Probabilistic and Robust Engineering Design #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1909.09250

openalex publication_date 2019/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the distribution function of the time of explosion of\na stochastic differential equation modeling the length of the dominant crack\ndue to fatigue. The main novelty is that initial condition is regarded as an\nanticipating random variable and the stochastic integral is in the forward\nsense. Under suitable conditions, we use the substitution formula from Russo\nand Vallois to find the local solution of this equation. Then, we find the law\nof blow up time by proving some results on barrier crossing probabilities of\nBrownian bridge.\n

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