| Description |
1 online resource (xx, 437 pages) : illustrations (chiefly color) |
| Series |
Interdisciplinary mathematical sciences ; v. 12 |
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Interdisciplinary mathematical sciences ; v. 12.
|
| Contents |
1. Stochastic geometric partial differential equations / Zdzislaw Brzezniak, Beniamin Goldys and Martin Ondrejat -- 2. Rough paths on manifolds / Thomas Cass, Christian Litterer and Terry Lyons -- 3. Averaging, homogenization and slow manifolds for stochastic partial differential equations / Jinqiao Duan, Anthony Roberts and Wei Wang -- 4. A Burgers-Zeldovich model for the formation of planetesimals via Nelson's stochastic mechanics / Richard Durran [and others] -- 5. Two problems concerning Brownian motion on a complete Riemannian manifold / Elton P. Hsu -- 6. Sticky shuffle product Hopf algebras and their stochastic representations / Robin Hudson -- 7. Chain rules for Levy flows and Kolmogorov equations for associated jump-diffusions / Hiroshi Kunita -- 8. The stochastic differential equation approach to analysis on path space / Xue-Mei Li -- 9. Pathwise properties of random quadratic mapping / Peng Lian and Huaizhong Zhao -- 10. Invariant manifolds for infinite dimensional random dynamical systems / Kening Lu and Bjorn Schmalfub -- 11. Some topics on Dirichlet forms / Zhi-Ming Ma and Wei Sun -- 12. Hamilton-Jacobi theory and the stochastic elementary formula / Andrew Neate and Aubrey Truman |
| Summary |
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 phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc |
| Bibliography |
Includes bibliographical references |
| Subject |
Stochastic analysis.
|
|
MATHEMATICS -- Probability & Statistics -- General.
|
|
Stochastic analysis
|
| Form |
Electronic book
|
| Author |
Zhao, Huaizhong
|
|
Truman, A. (Aubrey)
|
|
Elworthy, K. D
|
| ISBN |
9789814360920 |
|
9814360929 |
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