Constants in the asymptotics of small deviation probabilities for Gaussian processes and fields

Fatalov, V. R.

doi:10.1070/rm2003v058n04abeh000643

Cited by 26 publications

(18 citation statements)

References 127 publications

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“…Furthermore, there is only a rough understanding that P g becomes more accurate as the boundary diverges. Both of these issues are addressed formally in the following theorem, due originally to Fatalov (1992Fatalov ( , 1993. Note that an attractive feature of Theorem 2 is that convergence to the true boundary crossing probability is at a relatively quick rate as the boundary diverges: in Durbin (1985, p. 113), it could only be estimated that P g approaches P 1 at a polynomial rate.…”

Section: By the Definition Ofmentioning

confidence: 99%

“…The work of Tyurin (1985) was perhaps the first such derivation, but the focus here will be on the work of Fatalov (1992Fatalov ( , 1993 and Piterbarg (1996). The reason for this is that the theory underlying the result is quite general and has roots that are more clearly probabilistic -the work of Tyurin relies on the solution to boundary value problems and can usually only be applied in the same situations as Durbin's P g , while Fatalov's work allows one to compute probabilities not available via Durbin's or Tyurin's formulation of the solution.…”

Section: Imagine a Hypothetical Regression Of Y(s) On Y(t) Without Amentioning

confidence: 99%

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A comparison of alternative approaches to sup-norm goodness of fit tests with estimated parameters

Parker

2010

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. for Gaussian random fields and for Gauss-Markov processes. These adjustment techniques are also related to the transformation methodology proposed by Khmaladze (1981) through the score function of the parametric model. Monte Carlo experiments suggest that these two testing strategies are roughly comparable to one another and more powerful than a simple bootstrap procedure. Terms of use: Documents in

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Section: By the Definition Ofmentioning

confidence: 99%

Section: Imagine a Hypothetical Regression Of Y(s) On Y(t) Without Amentioning

confidence: 99%

A comparison of alternative approaches to sup-norm goodness of fit tests with estimated parameters

Parker

2010

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“…For example, assume that ξ( ) is the fractional Brownian motion with the Hurst parameter H and G is a unit ball in the sup-norm. Then One can find the exact expression for in [4], for example. Using results mentioned in [4], one can also consider Hölder norms instead of the sup-norm.…”

Section: Remark 26mentioning

confidence: 99%

“…Then One can find the exact expression for in [4], for example. Using results mentioned in [4], one can also consider Hölder norms instead of the sup-norm. In the same way, one may also apply results on small ball probabilities for the Wiener process in weighted sup-norms and L -norms, the Bessel processes in the sup-norm and weighted sup-norms (see [4]).…”

Section: Remark 26mentioning

confidence: 99%