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Träfflista för sökning "L773:0091 1798 srt2:(1975-1979)"

Sökning: L773:0091 1798 > (1975-1979)

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1.
  • Lindgren, Georg (författare)
  • Prediction from a random time point
  • 1975
  • Ingår i: Annals of Probability. - 0091-1798. ; 3:3, s. 412-423
  • Tidskriftsartikel (refereegranskat)abstract
    • In prediction (Wiener-, Kalman-) of a random normal process $\{X(t), t \in R\}$ it is normally required that the time $t_0$ from which prediction is made does not depend on the values of the process. If prediction is made only from time points at which the process takes a certain value $u,$ given a priori, ("prediction under panic"), the Wiener-prediction is not necessarily optimal; optimal should then mean best in the long run, for each single realization. The main theorem in this paper shows that when predicting only from upcrossing zeros $t_\nu$, the Wiener-prediction gives optimal prediction of $X(t_\nu + t)$ as $t_\nu$ runs through the set of zero upcrossings, if and only if the derivative $X'(t_\nu)$ at the crossing points is observed. The paper also gives the conditional distribution from which the optimal predictor can be computed.
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2.
  • Lindgren, Georg, et al. (författare)
  • Weak convergence of high level crossings and maxima for one or more Gaussian processes
  • 1975
  • Ingår i: Annals of Probability. - : Institute of Mathematical Statistics. - 0091-1798. ; 3:6, s. 961-978
  • Tidskriftsartikel (refereegranskat)abstract
    • Weak convergence of the multivariate point process of upcrossings of several high levels by a stationary Gaussian process is established. The limit is a certain multivariate Poisson process. This result is then used to determine the joint asymptotic distribution of heights and locations of the highest local maxima over an increasing interval. The results are generalized to upcrossings and local maxima of two dependent Gaussian processes. To prevent nuisance jitter from hiding the overall structure of crossings and maxima the above results are phrased in terms of varepsilon-crossings and varepsilon-maxima, but it is shown that under suitable regularity conditions the results also hold for ordinary upcrossings and maxima.
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  • Resultat 1-2 av 2
Typ av publikation
tidskriftsartikel (2)
Typ av innehåll
refereegranskat (2)
Författare/redaktör
Lindgren, Georg (2)
de Maré, Jacques (1)
Rootzén, Holger (1)
Lärosäte
Lunds universitet (2)
Språk
Engelska (2)
Forskningsämne (UKÄ/SCB)
Naturvetenskap (2)
År
1975 (2)

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