Abstract:
It is shown by means of examples that the Rice series may be used for representation of P{ξt:ξt⩽0,t∈[0,T]} in the cases of nondifferentiable processes ξt or processes ξt with purely discontinuous spectrum.
\Bibitem{Mir83}
\by R.~N.~Miro{\v s}in
\paper The using of Rice series
\jour Teor. Veroyatnost. i Primenen.
\yr 1983
\vol 28
\issue 4
\pages 679--690
\mathnet{http://mi.mathnet.ru/tvp2216}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=726894}
\zmath{https://zbmath.org/?q=an:0561.60039|0529.60031}
\transl
\jour Theory Probab. Appl.
\yr 1984
\vol 28
\issue 4
\pages 714--726
\crossref{https://doi.org/10.1137/1128070}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1984TV66700006}
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https://www.mathnet.ru/eng/tvp2216
https://www.mathnet.ru/eng/tvp/v28/i4/p679
This publication is cited in the following 3 articles:
Level Sets and Extrema of Random Processes and Fields, 2009, 373
Jean-Marc Azaïs, Mario Wschebor, In and Out of Equilibrium, 2002, 321
Jean-Marc Azaïs, Mario Wschebor, “Une formule pour calculer la distribution du maximum d'un processus stochastique”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 324:2 (1997), 225
Citation in format AMSBIB
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