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001			21736404
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006			m |o d |
007			cr |||||||||||
008			140915s2014 gw |||| o |||| 0|eng
010			_a 2019754087
020			_a9783319095899 (Pbk)
024	7		_a10.1007/978-3-319-09590-5 _2doi
035			_a21736404
035			_a(DE-He213)978-3-319-09590-5
040			_aDLC _beng _epn _erda _cIISERB
072		7	_aMAT029000 _2bisacsh
072		7	_aPBT _2bicssc
072		7	_aPBT _2thema
072		7	_aPBWL _2thema
082	0	4	_a519.2 B750F _223
100	1		_aBremaud, Pierre. _932627
245	1	0	_aFourier Analysis and Stochastic Processes / _cby Pierre Brémaud.
260			_aSwitzarland: _bSpringer, _c2014.
300			_a(XIII, 385 pages 2 illustrations)
490	1		_aUniversitext, _x0172-5939
505	0		_aFourier analysis of functions -- Fourier theory of probability distributions -- Fourier analysis of stochastic processes -- Fourier analysis of time series -- Power spectra of point processes.
520			_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.
650		0	_aFourier analysis. _932628
650		0	_aProbabilities. _932629
650	1	4	_aProbability Theory and Stochastic Processes. _932630
650	2	4	_aFourier Analysis. _932631
776	0	8	_iPrint version: _tFourier analysis and stochastic processes. _z9783319095899 _w(DLC) 2014946193
776	0	8	_iPrinted edition: _z9783319095899
776	0	8	_iPrinted edition: _z9783319095912
830		0	_aUniversitext, _932632
906			_a0 _bibc _corigres _du _encip _f20 _gy-gencatlg
942			_2ddc _cBK
999			_c10984 _d10984