LEADER 04046nam0 22005893i 450 001 VAN00268179 005 20260630102906.564 017 70$2N$a9781461262756 035 40$a848732047 100 $a20231130d1978 |0itac50 ba 101 $aeng 102 $aUS 105 $a|||| ||||| 181 $ai$b e 182 $ab 183 $acr 200 1 $aGaussian Random Processes$fI. A. Ibragimov, Y. A. Rozanov$gTranslated by A. B. Aries 210 $aNew York$cSpringer-Verlag$d1978 215 $ax, 277 p.$cill.$d24 cm 327 $aThe book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva­ lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par­ ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate". The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of "distinguishing a signal from stationary noise". Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam­ ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys­ tematic presentation of the basic results can be found, for instance, in [23]). In this book we have considered Gaussian stationary processes and arrived, we believe, at rather definite solutions. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes. 410 1$1001VAN00076490$12001 $aStochastic modelling and applied probability$1210 $aNew York [etc.]$cSpringer$d1975-2024.$v9 500 1$3VAN00268182$aGaussovskie slu?ajnye processy$93597431 606 $a60G10$xStationary stochastic processes [MSC 2020]$3VANC021552$2MF 606 $a60G15$xGaussian processes [MSC 2020]$3VANC020010$2MF 606 $a60G35$xSignal detection and filtering (aspects of stochastic processes) [MSC 2020]$3VANC021485$2MF 610 $aErgodic theory$9KW:K 610 $aGaussian measures$9KW:K 610 $aGaussian processes$9KW:K 610 $aMixing$9KW:K 610 $aProbability measures$9KW:K 610 $aRandom functions$9KW:K 610 $aStationary processes$9KW:K 620 $aUS$dNew York$3VANL000011 700 1$aIbragimov$bIlldar A.$3VANV217821$0441478 701 1$aRozanov$bYurii A.$3VANV082116$01427702 702 1$aAries$bAntony B.$3VANV215891$4730 712 $aSpringer $3VANV108073$4650 790 1$aRozanov, Yuri? Anatol?evich$zRozanov, Yurii A.$3VANV220338 790 1$aRozanov, Yu. A.$zRozanov, Yurii A.$3VANV260355 790 1$aRozanov, Y. A.$zRozanov, Yurii A.$3VANV260356 790 1$aRosanow, J. A.$zRozanov, Yurii A.$3VANV260357 790 1$aRosanov, Yu. A.$zRozanov, Yurii A.$3VANV260358 790 1$aAries, A. B.$zAries, Antony B.$3VANV266058 790 1$aAries, A.B.$zAries, Antony B.$3VANV266059 801 $aIT$bSOL$c20260911$gRICA 856 4 $uhttps://doi.org/10.1007/978-1-4612-6275-6$zE-book ? Accesso al full-text attraverso riconoscimento IP di Ateneo, proxy e/o Shibboleth 899 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$1IT-CE0120$2VAN08 912 $fN 912 $aVAN00268179 950 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$d08DLOAD e-book 7405 $e08eMF7405 20231204 996 $aGaussovskie slu?ajnye processy$93597431 997 $aUNICAMPANIA