000 03311nam a22004575i 4500
001 978-3-642-24939-6
003 DE-He213
005 20140220083304.0
007 cr nn 008mamaa
008 120110s2012 gw | s |||| 0|eng d
020 _a9783642249396
_9978-3-642-24939-6
024 7 _a10.1007/978-3-642-24939-6
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aLifshits, Mikhail.
_eauthor.
245 1 0 _aLectures on Gaussian Processes
_h[electronic resource] /
_cby Mikhail Lifshits.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2012.
300 _aX, 121p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringerBriefs in Mathematics,
_x2191-8198
505 0 _aPreface -- 1.Gaussian Vectors and Distributions -- 2.Examples of Gaussian Vectors, Processes and Distributions -- 3.Gaussian White Noise and Integral Representations -- 4.Measurable Functionals and the Kernel -- 5.Cameron-Martin Theorem -- 6.Isoperimetric Inequality -- 7.Measure Concavity and Other Inequalities -- 8.Large Deviation Principle -- 9.Functional Law of the Iterated Logarithm -- 10.Metric Entropy and Sample Path Properties -- 11.Small Deviations -- 12.Expansions of Gaussian Vectors -- 13.Quantization of Gaussian Vectors -- 14.Invitation to Further Reading -- References.
520 _aGaussian processes can be viewed as a  far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of Gaussian processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such as small deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs.
650 0 _aMathematics.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642249389
830 0 _aSpringerBriefs in Mathematics,
_x2191-8198
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-24939-6
912 _aZDB-2-SMA
999 _c102360
_d102360