LEADER 03843nam 22006615 450 001 9910299981903321 005 20251117075808.0 010 $a3-319-09590-0 024 7 $a10.1007/978-3-319-09590-5 035 $a(CKB)3710000000249659 035 $a(Springer)9783319095905 035 $a(MH)014199342-1 035 $a(SSID)ssj0001354133 035 $a(PQKBManifestationID)11810431 035 $a(PQKBTitleCode)TC0001354133 035 $a(PQKBWorkID)11322889 035 $a(PQKB)11734750 035 $a(DE-He213)978-3-319-09590-5 035 $a(MiAaPQ)EBC6314889 035 $a(MiAaPQ)EBC5587570 035 $a(Au-PeEL)EBL5587570 035 $a(OCoLC)891931722 035 $a(PPN)181352990 035 $a(EXLCZ)993710000000249659 100 $a20140915d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFourier Analysis and Stochastic Processes /$fby Pierre Brémaud 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (XIII, 385 p. 2 illus.)$conline resource 225 1 $aUniversitext,$x0172-5939 300 $aIncludes index. 311 08$a3-319-09589-7 327 $aFourier analysis of functions -- Fourier theory of probability distributions -- Fourier analysis of stochastic processes -- Fourier analysis of time series -- Power spectra of point processes. 330 $aThis work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spaces in the first chapter) make the book self-contained. Each chapter has an exercise section, which makes Fourier Analysis and Stochastic Processes suitable for a graduate course in applied mathematics, as well as for self-study. 410 0$aUniversitext,$x0172-5939 606 $aProbabilities 606 $aFourier analysis 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 615 0$aProbabilities. 615 0$aFourier analysis. 615 14$aProbability Theory and Stochastic Processes. 615 24$aFourier Analysis. 676 $a519.2 700 $aBre?maud$b Pierre$4aut$4http://id.loc.gov/vocabulary/relators/aut$00 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299981903321 996 $aFourier analysis and stochastic processes$91409900 997 $aUNINA 999 $aThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress