| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNISA996485661203316 |
|
|
Autore |
Lee Haesung |
|
|
Titolo |
Analytic theory of Itô-stochastic differential equations with non-smooth coefficients / / Haesung Lee, Wilhelm Stannat, Gerald Trutnau |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Singapore : , : Springer, , [2022] |
|
©2022 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Descrizione fisica |
|
1 online resource (139 pages) |
|
|
|
|
|
|
Collana |
|
SpringerBriefs in probability and mathematical statistics |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Stochastic differential equations |
Equacions diferencials estocàstiques |
Llibres electrònics |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
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. |
|
|
|
|
|
| |