LEADER 03489nam 2200493 450 001 9910590068703321 005 20230717145357.0 010 $a981-19-3831-8 035 $a(MiAaPQ)EBC7078084 035 $a(Au-PeEL)EBL7078084 035 $a(CKB)24748192400041 035 $a(PPN)264193849 035 $a(EXLCZ)9924748192400041 100 $a20230113d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnalytic theory of Ito?-stochastic differential equations with non-smooth coefficients /$fHaesung Lee, Wilhelm Stannat, Gerald Trutnau 210 1$aSingapore :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (139 pages) 225 1 $aSpringerBriefs in probability and mathematical statistics 311 08$aPrint version: Lee, Haesung Analytic Theory of Itô-Stochastic Differential Equations with Non-Smooth Coefficients Singapore : Springer,c2022 9789811938306 320 $aIncludes bibliographical references and index. 327 $aIntro -- Acknowledgments -- Contents -- Notations and Conventions -- 1 Introduction -- 1.1 Methods and Results -- 1.2 Organization of the Book -- 2 The Abstract Cauchy Problem in Lr-Spaces with Weights -- 2.1 The Abstract Setting, Existence and Uniqueness -- 2.1.1 Framework and Basic Notations -- 2.1.2 Existence of Maximal Extensions on Rd -- 2.1.2.1 Existence of Maximal Extensions on Relatively Compact Subsets VRd -- 2.1.2.2 Existence of Maximal Extensions on the Full Domain Rd -- 2.1.3 Uniqueness of Maximal Extensions on Rd -- 2.1.3.1 Uniqueness of (L, D(L0)0,b) -- 2.1.3.2 Uniqueness of (L, C0?(Rd )) -- 2.2 Existence and Regularity of Densities to Infinitesimally Invariant Measures -- 2.2.1 Class of Admissible Coefficients and the Main Theorem -- 2.2.2 Proofs -- 2.2.3 Discussion -- 2.3 Regular Solutions to the Abstract Cauchy Problem -- 2.4 Irreducibility of Solutions to the Abstract Cauchy Problem -- 2.5 Comments and References to Related Literature -- 3 Stochastic Differential Equations -- 3.1 Existence -- 3.1.1 Regular Solutions to the Abstract Cauchy Problem as Transition Functions -- 3.1.2 Construction of a Hunt Process -- 3.1.3 Krylov-type Estimate -- 3.1.4 Identification of the Stochastic Differential Equation -- 3.2 Global Properties -- 3.2.1 Non-explosion Results and Moment Inequalities -- 3.2.2 Transience and Recurrence -- 3.2.3 Long Time Behavior: Ergodicity, Existence and Uniqueness of Invariant Measures, Examples/Counterexamples -- 3.3 Uniqueness -- 3.3.1 Pathwise Uniqueness and Strong Solutions -- 3.3.2 Uniqueness in Law (Via L1-Uniqueness) -- 3.4 Comments and References to Related Literature -- 4 Conclusion and Outlook -- References -- Index. 410 0$aSpringer briefs in probability and mathematical statistics. 606 $aStochastic differential equations 606 $aEquacions diferencials estocàstiques$2thub 608 $aLlibres electrònics$2thub 615 0$aStochastic differential equations. 615 7$aEquacions diferencials estocàstiques 676 $a519.2 700 $aLee$b Haesung$01254528 702 $aStannat$b Wilhelm 702 $aTrutnau$b Gerald 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910590068703321 996 $aAnalytic theory of Ito?-stochastic differential equations with non-smooth coefficients$93362641 997 $aUNINA