LEADER 04627nam 2200709 a 450 001 9910790493303321 005 20230801223626.0 010 $a1-283-85795-2 010 $a3-11-027898-7 024 7 $a10.1515/9783110278989 035 $a(CKB)2670000000211124 035 $a(EBL)893930 035 $a(OCoLC)796384288 035 $a(SSID)ssj0000676889 035 $a(PQKBManifestationID)12328659 035 $a(PQKBTitleCode)TC0000676889 035 $a(PQKBWorkID)10684000 035 $a(PQKB)10107666 035 $a(MiAaPQ)EBC893930 035 $a(DE-B1597)175341 035 $a(OCoLC)812403796 035 $a(DE-B1597)9783110278989 035 $a(Au-PeEL)EBL893930 035 $a(CaPaEBR)ebr10582309 035 $a(CaONFJC)MIL417045 035 $a(EXLCZ)992670000000211124 100 $a20120319d2012 uy 0 101 0 $aeng 135 $aurun#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aBrownian motion$b[electronic resource] $ean introduction to stochastic processes /$fRene? L. Schilling, Lothar Partzsch ; with a chapter on simulation by Bjo?rn Bo?ttcher 210 $aBerlin ;$aBoston $cDe Gruyter$dc2012 215 $a1 online resource (396 p.) 225 1 $aDe Gruyter graduate 300 $aDescription based upon print version of record. 311 0 $a3-11-027889-8 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tPreface --$tContents --$tDependence chart --$tIndex of notation --$tChapter 1. Robert Brown's new thing --$tChapter 2. Brownian motion as a Gaussian process --$tChapter 3. Constructions of Brownian motion --$tChapter 4. The canonical model --$tChapter 5. Brownian motion as a martingale --$tChapter 6. Brownian motion as a Markov process --$tChapter 7. Brownian motion and transition semigroups --$tChapter 8. The PDE connection --$tChapter 9. The variation of Brownian paths --$tChapter 10. Regularity of Brownian paths --$tChapter 11. The growth of Brownian paths --$tChapter 12. Strassen's Functional Law of the Iterated Logarithm --$tChapter 13. Skorokhod representation --$tChapter 14. Stochastic integrals: L2-Theory --$tChapter 15. Stochastic integrals: beyond L2T --$tChapter 16. Itô's formula --$tChapter 17. Applications of Itô's formula --$tChapter 18. Stochastic differential equations --$tChapter 19. On diffusions --$tChapter 20. Simulation of Brownian motion /$rBöttcher, Björn --$tAppendix --$tIndex 330 $aBrownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance. Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors' aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs. This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion. 410 0$aDe Gruyter graduate. 606 $aBrownian motion processes 606 $aStochastic processes 610 $aBrownian Motion. 610 $aNumerical Simulation. 610 $aStochastic Calculus. 610 $aStochastic Process. 615 0$aBrownian motion processes. 615 0$aStochastic processes. 676 $a519.2/33 686 $aSK 820$2rvk 700 $aSchilling$b Rene? L$0478394 701 $aPartzsch$b Lothar$f1945-$01496144 701 $aBo?ttcher$b Bjo?rn$0479681 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910790493303321 996 $aBrownian motion$93720650 997 $aUNINA