LEADER 02912nam 22005295 450 001 9910299963703321 005 20200704082045.0 010 $a3-319-02642-9 024 7 $a10.1007/978-3-319-02642-8 035 $a(CKB)3710000000078758 035 $a(SSID)ssj0001091380 035 $a(PQKBManifestationID)11993002 035 $a(PQKBTitleCode)TC0001091380 035 $a(PQKBWorkID)11028946 035 $a(PQKB)10283218 035 $a(DE-He213)978-3-319-02642-8 035 $a(MiAaPQ)EBC3107054 035 $a(PPN)176106472 035 $a(EXLCZ)993710000000078758 100 $a20131202d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMultiple Wiener-Itô Integrals $eWith Applications to Limit Theorems /$fby Péter Major 205 $a2nd ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (XIII, 126 p. 4 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v849 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-02641-0 330 $aThe goal of this Lecture Note is to prove a new type of limit theorems for normalized sums of strongly dependent random variables that play an important role in probability theory or in statistical physics. Here non-linear functionals of stationary Gaussian fields are considered, and it is shown that the theory of Wiener?Itô integrals provides a valuable tool in their study. More precisely, a version of these random integrals is introduced that enables us to combine the technique of random integrals and Fourier analysis. The most important results of this theory are presented together with some non-trivial limit theorems proved with their help. This work is a new, revised version of a previous volume written with the goalof giving a better explanation of some of the details and the motivation behind the proofs. It does not contain essentially new results; it was written to give a better insight to the old ones. In particular, a more detailed explanation of generalized fields is included to show that what is at the first sight a rather formal object is actually a useful tool for carrying out heuristic arguments. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v849 606 $aProbabilities 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aProbabilities. 615 14$aProbability Theory and Stochastic Processes. 676 $a519.2 700 $aMajor$b Péter$4aut$4http://id.loc.gov/vocabulary/relators/aut$048603 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299963703321 996 $aMultiple Wiener-Itô integrals$981079 997 $aUNINA LEADER 01709nam 22004813 450 001 9910921016403321 005 20251116213944.0 010 $a9789819989171 010 $a9819989175 035 $a(CKB)37133703000041 035 $a(MiAaPQ)EBC31875769 035 $a(Au-PeEL)EBL31875769 035 $a(OCoLC)1482833418 035 $a(EXLCZ)9937133703000041 100 $a20250113d2025 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFault Diagnosis and Prognostics Based on Cognitive Computing and Geometric Space Transformation 205 $a1st ed. 210 1$aSingapore :$cSpringer,$d2025. 210 4$d©2024. 215 $a1 online resource (503 pages) 225 1 $aIntelligent Technologies and Robotics Series 311 08$a9789819989164 311 08$a9819989167 330 $aThis monograph introduces readers to new theories and methods applying cognitive computing and geometric space transformation to the field of fault diagnosis and prognostics.It summarizes the basic concepts and technical aspects of fault diagnosis and prognostics technology. 410 0$aIntelligent Technologies and Robotics Series 676 $a620.0044 700 $aLu$b Chen$01782350 701 $aTao$b Laifa$01782351 701 $aMa$b Jian$0551886 701 $aCheng$b Yujie$01782352 701 $aDing$b Yu$01589108 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910921016403321 996 $aFault Diagnosis and Prognostics Based on Cognitive Computing and Geometric Space Transformation$94308419 997 $aUNINA