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Introduction to Infinite Dimensional Stochastic Analysis

Author: Zhi-yuan Huang; J Yan
Publisher: Dordrecht : Springer Netherlands, 2000.
Series: Mathematics and Its Applications, 502.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book offers a concise introduction to the rapidly expanding field of infinite dimensional stochastic analysis. It treats Malliavin calculus and white noise analysis in a single book, presenting these two different areas in a unified setting of Gaussian probability spaces. Topics include recent results and developments in the areas of quasi-sure analysis, anticipating stochastic calculus, generalised operator  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Zhi-yuan Huang; J Yan
ISBN: 9789401141086 9401141088
OCLC Number: 851373497
Description: 1 online resource (xi, 296 pages).
Contents: I Foundations of Infinite Dimensional Analysis --
§1. Linear operators on Hilbert spaces --
§2. Fock spaces and second quantization --
§3. Countably normed spaces and nuclear spaces --
§4. Borel measures on topological linear spaces --
II Malliavin Calculus --
§1. Gaussian probability spaces and Wiener chaos decomposition --
§2. Differential calculus of functionals, gradient and divergence operators --
§3. Meyer's inequalities and some consequences --
§4. Densities of non-degenerate functionals --
III Stochastic Calculus of Variation for Wiener Functionals --
§1. Differential calculus of Itô functionals and regularity of heat kernels --
§2. Potential theory over Wiener spaces and quasi-sure analysis --
§3. Anticipating stochastic calculus --
IV General Theory of White Noise Analysis --
§1. General framework for white noise analysis --
§2. Characterization of functional spaces --
§3. Products and Wick products of functionals --
§4. Moment characterization of distributions and positive distributions --
V Linear Operators on Distribution Spaces --
§1. Analytic calculus for distributions --
§2. Continuous linear operators on distribution spaces --
§3. Integral kernel operators and integral kernel representation for operators --
§4. Applications to quantum physics --
Appendix A Hermite polynomials and Hermite functions --
Appendix B Locally convex spaces amd their dual spaces --
1. Semi-norms, norms and H-norms --
2. Locally convex topological linear spaces, bounded sets --
3. Projective topologies and projective limits --
4. Inductive topologies and inductive limits --
5. Dual spaces and weak topologies --
6. Compatibility and Mackey topology --
7. Strong topologies and reflexivity --
8. Dual maps --
9. Uniformly convex spaces and Banach-Saks' theorem --
Comments --
References --
Index of Symbols.
Series Title: Mathematics and Its Applications, 502.
Responsibility: by Zhi-yuan Huang, Jia-an Yan.

Abstract:

diffusion processes) and thus revealed the deep connection between theories of differential equations and stochastic processes. By virtue of Ito's stochastic differential equations one can construct  Read more...

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'The book is well written and nicely structured [...] will surely become a valuable resource for specialists in stochastic analysis as well as mathematical physicists.' Mathematical Reviews (2002)

 
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