LEADER 04446nam 22006375 450 001 9910349345503321 005 20200629174144.0 010 $a9789813297418 010 $a9813297417 024 7 $a10.1007/978-981-32-9741-8 035 $a(CKB)4100000008959075 035 $a(DE-He213)978-981-32-9741-8 035 $a(MiAaPQ)EBC5924208 035 $a(PPN)24860211X 035 $a(MiAaPQ)EBC31886884 035 $a(Au-PeEL)EBL31886884 035 $a(OCoLC)1117494727 035 $a(EXLCZ)994100000008959075 100 $a20190813d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aJump SDEs and the Study of Their Densities $eA Self-Study Book /$fby Arturo Kohatsu-Higa, Atsushi Takeuchi 205 $a1st ed. 2019. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2019. 215 $a1 online resource (XIX, 355 p. 6 illus.) 225 1 $aUniversitext,$x0172-5939 311 08$a9789813297401 311 08$a9813297409 327 $aReview of some basic concepts of probability theory -- Simple Poisson process and its corresponding SDEs -- Compound Poisson process and its associated stochastic calculus -- Construction of Lévy processes and their corresponding SDEs: The finite variation case -- Construction of Lévy processes and their corresponding SDEs: The infinite variation case -- Multi-dimensional Lévy processes and their densities -- Flows associated with stochastic differential equations with jumps -- Overview -- Techniques to study the density -- Basic ideas for integration by parts formulas -- Sensitivity formulas -- Integration by parts: Norris method -- A non-linear example: The Boltzmann equation -- Further hints for the exercises . 330 $aThe present book deals with a streamlined presentation of Lévy processes and their densities. It is directed at advanced undergraduates who have already completed a basic probability course. Poisson random variables, exponential random variables, and the introduction of Poisson processes are presented first, followed by the introduction of Poisson random measures in a simple case. With these tools the reader proceeds gradually to compound Poisson processes, finite variation Lévy processes and finally one-dimensional stable cases. This step-by-step progression guides the reader into the construction and study of the properties of general Lévy processes with no Brownian component. In particular, in each case the corresponding Poisson random measure, the corresponding stochastic integral, and the corresponding stochastic differential equations (SDEs) are provided. The second part of the book introduces the tools of the integration by parts formula for jump processes in basic settings and first gradually provides the integration by parts formula in finite-dimensional spaces and gives a formula in infinite dimensions. These are then applied to stochastic differential equations in order to determine the existence and some properties of their densities. As examples, instances of the calculations of the Greeks in financial models with jumps are shown. The final chapter is devoted to the Boltzmann equation. 410 0$aUniversitext,$x0172-5939 606 $aProbabilities 606 $aFunctional analysis 606 $aDifferential equations, Partial 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aProbabilities. 615 0$aFunctional analysis. 615 0$aDifferential equations, Partial. 615 14$aProbability Theory and Stochastic Processes. 615 24$aFunctional Analysis. 615 24$aPartial Differential Equations. 676 $a572.8293 700 $aKohatsu-Higa$b Arturo$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781866 702 $aTakeuchi$b Atsushi$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910349345503321 996 $aJump SDEs and the Study of Their Densities$92499540 997 $aUNINA