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035   $a(OCoLC)609842105
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035   $a(DE-B1597)9781400825103
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100   $a20020611d2002      uy             0
101 0 $aeng
135   $aurnn#---|u||u
181   $ctxt
182   $cc
183   $acr
200 10$aSelfsimilar processes$b[electronic resource] /$fPaul Embrechts and Makoto Maejima
205   $aCourse Book
210   $aPrinceton, N.J. $cPrinceton University Press$dc2002
215   $a1 online resource (123 p.)
225 1 $aPrinceton series in applied mathematics
300   $aDescription based upon print version of record.
311 0 $a0-691-09627-9 
320   $aIncludes bibliographical references and index.
327   $tFront matter --$tContents --$tChapter 1. Introduction --$tChapter 2. Some Historical Background --$tChapter 3. Self similar Processes with Stationary Increments --$tChapter 4. Fractional Brownian Motion --$tChapter 5. Self similar Processes with Independent Increments --$tChapter 6. Sample Path Properties of Self similar Stable Processes with Stationary Increments --$tChapter 7. Simulation of Self similar Processes --$tChapter 8. Statistical Estimation --$tChapter 9. Extensions --$tReferences --$tIndex
330   $aThe modeling of stochastic dependence is fundamental for understanding random systems evolving in time. When measured through linear correlation, many of these systems exhibit a slow correlation decay--a phenomenon often referred to as long-memory or long-range dependence. An example of this is the absolute returns of equity data in finance. Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful. Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications. After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that allows for further exploration. Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes. Numerous references point the reader to current applications. Though the text uses the mathematical language of the theory of stochastic processes, researchers and end-users from such diverse fields as mathematics, physics, biology, telecommunications, finance, econometrics, and environmental science will find it an ideal entry point for studying the already extensive theory and applications of selfsimilarity.
410  0$aPrinceton series in applied mathematics.
606   $aDistribution (Probability theory)
606   $aSelf-similar processes
610   $aAlmost surely.
610   $aApproximation.
610   $aAsymptotic analysis.
610   $aAutocorrelation.
610   $aAutoregressive conditional heteroskedasticity.
610   $aAutoregressive?moving-average model.
610   $aAvailability.
610   $aBenoit Mandelbrot.
610   $aBrownian motion.
610   $aCentral limit theorem.
610   $aChange of variables.
610   $aComputational problem.
610   $aConfidence interval.
610   $aCorrelogram.
610   $aCovariance matrix.
610   $aData analysis.
610   $aData set.
610   $aDetermination.
610   $aFixed point (mathematics).
610   $aForeign exchange market.
610   $aFractional Brownian motion.
610   $aFunction (mathematics).
610   $aGaussian process.
610   $aHeavy-tailed distribution.
610   $aHeuristic method.
610   $aHigh frequency.
610   $aInference.
610   $aInfimum and supremum.
610   $aInstance (computer science).
610   $aInternet traffic.
610   $aJoint probability distribution.
610   $aLikelihood function.
610   $aLimit (mathematics).
610   $aLinear regression.
610   $aLog?log plot.
610   $aMarginal distribution.
610   $aMathematica.
610   $aMathematical finance.
610   $aMathematics.
610   $aMethodology.
610   $aMixture model.
610   $aModel selection.
610   $aNormal distribution.
610   $aParametric model.
610   $aPower law.
610   $aProbability theory.
610   $aPublication.
610   $aRandom variable.
610   $aRegime.
610   $aRenormalization.
610   $aResult.
610   $aRiemann sum.
610   $aSelf-similar process.
610   $aSelf-similarity.
610   $aSimulation.
610   $aSmoothness.
610   $aSpectral density.
610   $aSquare root.
610   $aStable distribution.
610   $aStable process.
610   $aStationary process.
610   $aStationary sequence.
610   $aStatistical inference.
610   $aStatistical physics.
610   $aStatistics.
610   $aStochastic calculus.
610   $aStochastic process.
610   $aTechnology.
610   $aTelecommunication.
610   $aTextbook.
610   $aTheorem.
610   $aTime series.
610   $aVariance.
610   $aWavelet.
610   $aWebsite.
615  0$aDistribution (Probability theory)
615  0$aSelf-similar processes.
676   $a519.2/4
686   $aSK 820$2rvk
700   $aEmbrechts$b Paul$f1953-$028027
701   $aMaejima$b Makoto$0726746
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910779907303321
996   $aSelfsimilar processes$91422107
997   $aUNINA