Large Excursions of Gaussian Processes

Kac, Mark; Slepian, D.

doi:10.1214/aoms/1177706105

Cited by 146 publications

(59 citation statements)

References 6 publications

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“…conditioning introduced by Kac and Slepian (1959), and the so-called Slepian model process. For details of the latter we refer the reader to Lindgren's (1984) recent review.…”

Section: Behaviour Of X 2 Processes After a Level Crossingmentioning

confidence: 99%

Extrema and Level Crossings of x(2) Processes.

Aronowich¹,

Adler²

1985

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“…conditioning introduced by Kac and Slepian (1959), and the so-called Slepian model process. For details of the latter we refer the reader to Lindgren's (1984) recent review.…”

Section: Behaviour Of X 2 Processes After a Level Crossingmentioning

confidence: 99%

Extrema and Level Crossings of x(2) Processes.

Aronowich¹,

Adler²

1985

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“…Their work was clarified and generalized by Kac and Slepian [5]. The less general result of Volkonskii and Rozanov [10] was independently obtained about that time it is included in the monograph of Cramer and Leadbetter [4].…”

mentioning

confidence: 99%

Excursions above high levels for stationary Gaussian processes

Berman¹

1971

Pacific J. Math.

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“…It can be argued that the biased sampling distribution of dB(x) is represented by the distribution of the following stochastic process B u (t), t ∈ R: where random variable R has the Rayleigh distribution and is independent of dB(t), while B u (t) is understood as a random measure of [0, t], with the convention that for t < 0, the measure is understood as minus the measure of [t, 0]. The models that produce distributions observed at the crossings are often referred to as Slepian models introduced first in [13], see also [14] and [15] for a survey on this topic.…”

Section: A Noise At Gaussian Moving Average Crossingmentioning

confidence: 99%

Distributions at random events

Podgórski

Rychlik

2016

2016 Second International Conference on Event-Based Control, Communication, and Signal Processing (EBCCSP)

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Abstract-We review the generalized Rice formula approach to deriving long-run distributions of a variety of characteristics defined at random events defined on a stochastic process. While the approach stems from the same principle originally introduced by Rice for the level crossing intensity in a random signal, we show how it generalizes to more general contexts. Firstly, we discuss events defined on random surfaces through crossing levels of possibly multivariate valued stochastic fields. Secondly, the dynamics is introduced by adding time argument and introducing the concept of velocity measured at moving surface. Thirdly, extensions beyond the Gaussian model are shown by presenting effective models for sampling from the distribution of a nonGaussian noise observed at instances of level crossing by a process driven by this noise. The importance of these generalizations for engineering applications is illustrated through examples.

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Large Excursions of Gaussian Processes

Cited by 146 publications

References 6 publications

Extrema and Level Crossings of x(2) Processes.

Extrema and Level Crossings of x(2) Processes.

Excursions above high levels for stationary Gaussian processes

Distributions at random events

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