Maximizing the expected remaining useful lifetime of a weakly controlled device

Lefebvre, Mario

doi:10.1080/0305215x.2019.1660775

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Cited by 3 publications

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“…In [14], the author considered a model of this type for the amount of deterioration left in the case of a marine wind turbine. The function was chosen to be , where , and the environmental variable Y ( t ) was the wind speed.…”

Section: Introductionmentioning

confidence: 99%

A first-passage-place problem for integrated diffusion processes

Lefebvre

2023

J. Appl. Probab.

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Let ${\mathrm{d}} X(t) = -Y(t) \, {\mathrm{d}} t$ , where Y(t) is a one-dimensional diffusion process, and let $\tau(x,y)$ be the first time the process (X(t), Y(t)), starting from (x, y), leaves a subset of the first quadrant. The problem of computing the probability $p(x,y)\,:\!=\, \mathbb{P}[X(\tau(x,y))=0]$ is considered. The Laplace transform of the function p(x, y) is obtained in important particular cases, and it is shown that the transform can at least be inverted numerically. Explicit expressions for the Laplace transform of $\mathbb{E}[\tau(x,y)]$ and of the moment-generating function of $\tau(x,y)$ can also be derived.

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