LEADER 04008nam 22005775 450 001 9910300252703321 005 20251116145455.0 010 $a3-319-25820-6 024 7 $a10.1007/978-3-319-25820-1 035 $a(CKB)3710000000571739 035 $a(EBL)4323351 035 $a(SSID)ssj0001606931 035 $a(PQKBManifestationID)16314672 035 $a(PQKBTitleCode)TC0001606931 035 $a(PQKBWorkID)14897356 035 $a(PQKB)10675560 035 $a(DE-He213)978-3-319-25820-1 035 $a(MiAaPQ)EBC4323351 035 $a(PPN)191701998 035 $a(EXLCZ)993710000000571739 100 $a20160107d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDirichlet forms methods for Poisson point measures and Lévy processes $ewith emphasis on the creation-annihilation techniques /$fby Nicolas Bouleau, Laurent Denis 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (333 p.) 225 1 $aProbability Theory and Stochastic Modelling,$x2199-3130 ;$v76 300 $aDescription based upon print version of record. 311 08$a3-319-25818-4 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Notations and Basic Analytical Properties -- 1.Reminders on Poisson Random Measures, Lévy Processes and Dirichlet Forms -- 2.Dirichlet Forms and (EID) -- 3.Construction of the Dirichlet Structure on the Upper Space -- 4.The Lent Particle Formula and Related Formulae -- 5.Sobolev Spaces and Distributions on Poisson Space -- 6 -- Space-Time Setting and Processes -- 7.Applications to Stochastic Differential Equations driven by a Random Measure -- 8.Affine Processes, Rates Models -- 9.Non Poissonian Cases -- A. Error Structures -- B. The Co-Area Formula -- References. 330 $aA simplified approach to Malliavin calculus adapted to Poisson random measures is developed and applied in this book. Called the ?lent particle method? it is based on perturbation of the position of particles. Poisson random measures describe phenomena involving random jumps (for instance in mathematical finance) or the random distribution of particles (as in statistical physics). Thanks to the theory of Dirichlet forms, the authors develop a mathematical tool for a quite general class of random Poisson measures and significantly simplify computations of Malliavin matrices of Poisson functionals. The method gives rise to a new explicit calculus that they illustrate on various examples: it consists in adding a particle and then removing it after computing the gradient. Using this method, one can establish absolute continuity of Poisson functionals such as Lévy areas, solutions of SDEs driven by Poisson measure and, by iteration, obtain regularity of laws. The authors also give applications to error calculus theory. This book will be of interest to researchers and graduate students in the fields of stochastic analysis and finance, and in the domain of statistical physics. Professors preparing courses on these topics will also find it useful. The prerequisite is a knowledge of probability theory. 410 0$aProbability Theory and Stochastic Modelling,$x2199-3130 ;$v76 606 $aProbabilities 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aProbabilities. 615 14$aProbability Theory and Stochastic Processes. 676 $a519.2 700 $aBouleau$b Nicolas$4aut$4http://id.loc.gov/vocabulary/relators/aut$056550 702 $aDenis$b Laurent$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300252703321 996 $aDirichlet Forms Methods for Poisson Point Measures and Lévy Processes$92510891 997 $aUNINA