UID:
almafu_9959245515202883
Umfang:
1 online resource (458 p.)
ISBN:
981-4360-92-9
Serie:
Interdisciplinary mathematical sciences ; v. 12
Inhalt:
The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random pheno
Anmerkung:
Description based upon print version of record.
,
Editorial Foreword; Contents; A Biographical Note and Tribute to David Elworthy on His 70th Birthday; Edited Volumes; 1. Stochastic Geometric Partial Differential EquationsZdzisław Brze ́zniak, Beniamin Goldys and Martin Ondrej ́at; 1.1. Introduction; 1.2. Stochastic Geometric heat flow on S1 R+; 1.3. Proof of Theorem 1.1; 1.3.1. Differential Geometry preliminaries; 1.3.2. Existence of solutions to approximating equations; 1.3.3. Construction of a maximal local solution; 1.3.4. No explosion for approximate solutions; 1.4. Stochastic geometric wave equations; 1.4.1. Deterministic theory
,
1.4.2. Historical remarks1.4.3. Objectives; 1.5. Spatially homogeneous Wiener process; 1.6. Intrinsic and extrinsic solutions; 1.6.1. Posing the problem; 1.6.2. Extrinsic form; 1.6.3. Intrinsic form; 1.6.4. Extrinsic vs. Intrinsic; 1.7. Strong solutions in H2 loc H1 loc on R1+1; 1.8. Weak solutions in H1 loc L2 loc on R1+1; 1.9. Weak solutions in compact homogeneous spaces on R1+m; 1.10. Energy estimates; 1.11. Stochastic Landau-Lifschitz-Gilbert Equation; Acknowledgements; References; 2. Rough Paths on Manifolds Thomas Cass, Christian Litterer and Terry Lyons; 2.1. Introduction
,
2.2. Background: Rough paths on Banach spaces2.3. Lip- manifolds; 2.4. Rough paths on manifolds; 2.4.1. Introduction and motivation; 2.4.2. Definition and basic properties of rough paths on manifolds.; 2.4.3. Restriction and concatenations of rough paths on manifolds; 2.4.4. The support of a rough path on a manifold; 2.4.5. Rough paths on manifolds are concatenations of localisable rough paths.; 2.4.6. Proof of Theorem 2.7; 2.4.7. Proof of Theorem 2.8 and Corollary 2.2; 2.5. Rough differential equations on a manifold; 2.5.1. Geometric interpretation of the lift as an Ehresmann connection
,
2.5.2. Formal definition of the RDE solution via the connection2.6. Perspectives; References; 3. Averaging, Homogenization and Slow Manifolds for Stochastic Partial Differential Equations Jinqiao Duan, Anthony Roberts and Wei Wang; 3.1. Introduction; 3.2. Random invariant manifold reduction for SPDEs; 3.2.1. Lipschitz case; 3.2.2. Non-Lipschitz case; 3.3. Averaging reduction for SPDEs; 3.3.1. Averaging for slow-fast SPDEs; 3.3.2. Macroscopic reduction for stochastic reaction-diffusion equations: an application of averaging reduction
,
3.3.3. Large deviations: a further confirmation for averaged equation3.4. Homogenization for SPDEs; References; 4. A Burgers-Zeldovich Model for the Formation of Planetesimals via Nelson's Stochastic Mechanics Richard Durran, Andrew Neate, Aubrey Truman and Oleg Smolyanov; Dedication and Tribute to David Elworthy; 4.1. Introduction; 4.2. The First Epoch; 4.2.1. Stochastic mechanics for the atomic elliptic state; 4.2.2. A semiclassical celestial mechanics; 4.2.3. Internal states of the cloud and Markov chains; 4.3. The Second Epoch; 4.3.1. Burgers Equation with vorticity
,
4.3.2. Fluid density for small eccentricities
,
English
Weitere Ausg.:
ISBN 981-4360-91-0
Sprache:
Englisch
Fachgebiete:
Mathematik
