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Autore: | Lee Haesung |
Titolo: | Analytic theory of Itô-stochastic differential equations with non-smooth coefficients / / Haesung Lee, Wilhelm Stannat, Gerald Trutnau |
Pubblicazione: | Singapore : , : Springer, , [2022] |
©2022 | |
Descrizione fisica: | 1 online resource (139 pages) |
Disciplina: | 519.2 |
Soggetto topico: | Stochastic differential equations |
Equacions diferencials estocàstiques | |
Soggetto genere / forma: | Llibres electrònics |
Persona (resp. second.): | StannatWilhelm |
TrutnauGerald | |
Nota di bibliografia: | Includes bibliographical references and index. |
Nota di contenuto: | Intro -- 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. |
Titolo autorizzato: | Analytic theory of Itô-stochastic differential equations with non-smooth coefficients |
ISBN: | 981-19-3831-8 |
Formato: | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 996485661203316 |
Lo trovi qui: | Univ. di Salerno |
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