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Analytic theory of Itô-stochastic differential equations with non-smooth coefficients / / Haesung Lee, Wilhelm Stannat, Gerald Trutnau
| Analytic theory of Itô-stochastic differential equations with non-smooth coefficients / / Haesung Lee, Wilhelm Stannat, Gerald Trutnau |
| Autore | Lee Haesung |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (139 pages) |
| Disciplina | 519.2 |
| Collana | SpringerBriefs in probability and mathematical statistics |
| Soggetto topico |
Stochastic differential equations
Equacions diferencials estocàstiques |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-19-3831-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNINA-9910590068703321 |
Lee Haesung
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| Singapore : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Analytic theory of Itô-stochastic differential equations with non-smooth coefficients / / Haesung Lee, Wilhelm Stannat, Gerald Trutnau
| Analytic theory of Itô-stochastic differential equations with non-smooth coefficients / / Haesung Lee, Wilhelm Stannat, Gerald Trutnau |
| Autore | Lee Haesung |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (139 pages) |
| Disciplina | 519.2 |
| Collana | SpringerBriefs in probability and mathematical statistics |
| Soggetto topico |
Stochastic differential equations
Equacions diferencials estocàstiques |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-19-3831-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNISA-996485661203316 |
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Lee Haesung
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| Singapore : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Stochastic Partial Differential Equations and Related Fields [[electronic resource] ] : In Honor of Michael Röckner SPDERF, Bielefeld, Germany, October 10 -14, 2016 / / edited by Andreas Eberle, Martin Grothaus, Walter Hoh, Moritz Kassmann, Wilhelm Stannat, Gerald Trutnau
| Stochastic Partial Differential Equations and Related Fields [[electronic resource] ] : In Honor of Michael Röckner SPDERF, Bielefeld, Germany, October 10 -14, 2016 / / edited by Andreas Eberle, Martin Grothaus, Walter Hoh, Moritz Kassmann, Wilhelm Stannat, Gerald Trutnau |
| Edizione | [1st ed. 2018.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
| Descrizione fisica | 1 online resource (XX, 574 p. 5 illus.) |
| Disciplina | 519.2 |
| Collana | Springer Proceedings in Mathematics & Statistics |
| Soggetto topico |
Probabilities
Partial differential equations Mathematical physics Probability Theory and Stochastic Processes Partial Differential Equations Mathematical Applications in the Physical Sciences |
| ISBN | 3-319-74929-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Longer Contributions: V. Bogachev, Stationary Fokker-Planck-Kolmogorov equations -- M. Fukushima, Liouville property of harmonic functions of finite energy for Dirichlet forms -- B. Gess, Regularization and well-posedness by noise for ordinary and partial differential equations -- M. Gubinelli, N. Perkowski, An introduction to singular SPDEs -- N. Perkowski, M. Gubinelli, Probabilistic approach to the stochastic Burgers equation -- G. Da Prato, Fokker-Planck equations in Hilbert spaces -- Stochastic Partial Differential Equations and Regularity structures: Z. Brzezniak, G. Dhariwal, J. Hussain, M. Mariani, Stochastic and deterministic constrained partial differential equations -- P. Coupek, B. Maslowski, J. Šnupárková, SPDEs with Volterra Noise -- R. Dalang, Hitting probabilities for systems of stochastic PDEs: an overview -- C. Denis, T. Funaki, S. Yokoyama, Curvature motion perturbed by a direction-dependent colored noise -- N. Krylov, E. Priola, Poisson stochastic process and basic Schauder and Sobolev estimates in the theory of parabolic equations -- H. D. Luu, M. J. Garrido-Atienza, B. Schmalfuss, Dynamics of SPDE driven by a small fractional Brownian motion with Hurst parameter larger than ½ -- C. Marinelli, L. Scarpa, On the well-posedness of SPDEs with singular drift in divergence form -- L. J. de Naurois, A. Jentzen, T. Welti, Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations -- J. M. Tölle, Estimates for nonlinear stochastic partial differential equations with gradient noise via Dirichlet forms -- W. Yan, J. Duan, Random data Cauchy problem for some dispersive equations -- Lorenzo Zambotti, SPDEs and Renormalisation -- D. Zhang, Recent progress on stochastic nonlinear Schrödinger equations -- Stochastic Analysis including geometric aspects: V. Barbu, Generalized Solutions to Nonlinear Fokker-Planck Equations with Linear Drift -- Y. Bruned, I. Chevyrev, P. Friz, Examples of Renormalized SDEs -- K.D. Elworthy, Generalised Weitzenböck formulae for differential operators in Hörmander form -- M. Hofmanova, On the Rough Gronwall Lemma and its Applications -- X.-M. Li, Doubly Damped Stochastic Parallel translations and Hessian formulas -- M. Scheutzow, I. Vorkastner, Synchronization, Lyapunov exponents and stable manifolds for random dynamical Systems -- S. Shaposhnikov, Nonlinear Fokker-Planck-Kolmogorov equations for measures -- F.-Y. Wang, Coupling by Change of Measure, Harnack Inequality and Hypercontractivity -- X. Zhang, Multidimensional Singular Stochastic Differential Equations -- Dirichlet forms, Markov Processes and Potential theory: L. Beznea, I. Cimpean, L. Beznea, I. Cimpean. Invariant, super and quasi-martingale functions of a Markov process -- Z.-Q. Chen, T. Kumagai, J. Wang, Mean value inequalities for jump processes -- X. Chen, Z.-M. Ma, X. Peng, Positivity preserving semigroups and positivity preserving coercive forms -- N. Jacob, J. Harris, Some Thoughts and Investigations on Densities of One-Parameter Operator Semi-groups -- H. Kawabi, Strong uniqueness of Dirichlet operators related to stochastic quantization under exponential interactions in one-dimensional infinite volume -- V. Knopova, R. Schilling, A Probabilistic proof of the breakdown of Besov regularity in L-shaped domains -- T. Masayoshi, Symmetric Markov Processes with Tightness Property -- Applications including Mathematical Physics: J. Chen, M. Hinz, A. Teplyaev, From non-symmetric particle systems to non-linear PDEs on fractals -- Y. Kozitsky, Equilibrium States, Phase Transitions and Dynamics in Quantum Anharmonic Crystals -- X. Liu, B. Zegarlinski, On Continuous Coding -- H. Osada, Infinite-dimensional Stochastic Differential Equations with Symmetry -- R. Zhu, X. Zhu, Recent progress on the Dirichlet forms associated with stochastic quantization Problems. |
| Record Nr. | UNINA-9910300132703321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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