LEADER 05051nam 22007455 450 001 9910299988203321 005 20200703223147.0 010 $a3-319-07875-5 024 7 $a10.1007/978-3-319-07875-5 035 $a(CKB)3710000000262027 035 $a(EBL)1966827 035 $a(OCoLC)896837589 035 $a(SSID)ssj0001372665 035 $a(PQKBManifestationID)11767035 035 $a(PQKBTitleCode)TC0001372665 035 $a(PQKBWorkID)11305398 035 $a(PQKB)10977326 035 $a(MiAaPQ)EBC1966827 035 $a(DE-He213)978-3-319-07875-5 035 $a(PPN)182098834 035 $a(EXLCZ)993710000000262027 100 $a20141015d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aInference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion /$fby Corinne Berzin, Alain Latour, José R. León 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (195 p.) 225 1 $aLecture Notes in Statistics,$x0930-0325 ;$v216 300 $aDescription based upon print version of record. 311 $a3-319-07874-7 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $a1. Introduction -- 2. Preliminaries -- 3. Estimation of the Parameters -- 4. Simulation Algorithms and Simulation Studies -- 5. Proofs of all the results -- A. Complementary Results -- A.1. Introduction -- A.2. Proofs -- B. Tables and Figures Related to the Simulation Studies -- C. Some Pascal Procedures and Functions -- References -- Index. 330 $aThis book is devoted to a number of stochastic models that display scale invariance. It primarily focuses on three issues: probabilistic properties, statistical estimation and simulation of the processes considered. It will be of interest to probability specialists, who will find here an uncomplicated presentation of statistics tools, and to those statisticians who wants to tackle the most recent theories in probability in order to develop Central Limit Theorems in this context; both groups will also benefit from the section on simulation. Algorithms are described in great detail, with a focus on procedures that is not usually found in mathematical treatises. The models studied are fractional Brownian motions and processes that derive from them through stochastic differential equations. Concerning the proofs of the limit theorems, the ?Fourth Moment Theorem? is systematically used, as it produces rapid and helpful proofs that can serve as models for the future. Readers will also find elegant and new proofs for almost sure convergence. The use of diffusion models driven by fractional noise has been popular for more than two decades now. This popularity is due both to the mathematics itself and to its fields of application. With regard to the latter, fractional models are useful for modeling real-life events such as value assets in financial markets, chaos in quantum physics, river flows through time, irregular images, weather events, and contaminant diffus ion problems. 410 0$aLecture Notes in Statistics,$x0930-0325 ;$v216 606 $aStatistics  606 $aProbabilities 606 $aComputer simulation 606 $aStatistical Theory and Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/S11001 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aSimulation and Modeling$3https://scigraph.springernature.com/ontologies/product-market-codes/I19000 606 $aStatistics for Business, Management, Economics, Finance, Insurance$3https://scigraph.springernature.com/ontologies/product-market-codes/S17010 606 $aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/S17020 615 0$aStatistics . 615 0$aProbabilities. 615 0$aComputer simulation. 615 14$aStatistical Theory and Methods. 615 24$aProbability Theory and Stochastic Processes. 615 24$aSimulation and Modeling. 615 24$aStatistics for Business, Management, Economics, Finance, Insurance. 615 24$aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. 676 $a519.22 700 $aBerzin$b Corinne$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721288 702 $aLatour$b Alain$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aLeón$b José R$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299988203321 996 $aInference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion$92535770 997 $aUNINA