Holdings: Analysis on Gaussian spaces

Analysis on Gaussian spaces:

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Bibliographic Details
Main Author:	Hu, Yaozhong (Author)
Format:	Book
Language:	English
Published:	New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2017]
Subjects:	Maßtheorie Wahrscheinlichkeitsrechnung Gauß-Maß
Online Access:	Inhaltsverzeichnis
Physical Description:	xi, 470 Seiten
ISBN:	9789813142176

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MARC


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adam_text	Contents Preface vii 1. Introduction 1 2. Garsia-Rodemich-Rumsey Inequality 7 2.1 Metric Garsia-Rodemich-Rumsey Inequality............. 7 2.2 Volume Metric Garsia-Rodemich-Rumsey Inequality ... 11 2.3 Sample Path Holder Continuity of Random Fields....... 16 3. Analysis With Respect to Gaussian Measure in 19 3.1 Gaussian Measure in .................................... 19 3.2 Some Inequalities Related to Gaussian Measure........ 21 3.3 Brunn-Minkowski Inequality........................... 27 3.4 Hermite Polynomials.................................. 35 3.5 Spectral Gap and Logarithmic Sobolev Inequalities ... 43 3.6 Variance Identity and Inequality ....................... 47 3.7 Correlation Inequality............................... 48 3.8 Hyp ercontr activity................................. 51 3.9 Hermite Polynomials in Physics and Hermite Functions . 54 3.10 Segal-Bargmann Space and Complex Hermite Polynomials 58 3.11 Segal-Bargmann Transform............................. 63 4. Gaussian Measures on Banach Space 67 4.1 Random Variables in Banach Space..................... 67 4.2 Abstract Wiener Space................................ 80 4.3 Canonical Wiener Space............................... 88 ix 90 96 103 103 112 117 126 133 139 153 153 163 169 177 182 187 194 201 211 219 219 231 236 241 257 265 268 273 273 276 280 290 Analysis on Gaussian space 4.4 Right Tail Estimate.................................... 4.5 Small Ball (Left Tail) Estimate........................ Nonlinear Functionals on Abstract Wiener Space 5.1 Fock Space and Chaos Expansion......................... 5.2 Polarization........................................... 5.3 Multiple WienerTt6 Integrals........................... 5.4 Multiple Stratonovich Integrals........................ 5.5 Right Tail Estimate for Homogeneous Chaos.............. 5.6 Chaos Expansion of Exit Time and Skeleton of Wiener Functional............................................. Analysis of Nonlinear Wiener Functionals 6.1 Gross-Sobolev Derivatives.............................. 6.2 Divergence Operator.................................... 6.3 Regularity of Density of Wiener Functional............. 6.4 Girsanov Transformation: Finite Dimension.............. 6.5 Girsanov-Ramer Theorem in Abstract Wiener Space . . . 6.6 Wick Product........................................... 6.7 Wick Renormalization................................... 6.8 (Noncommutative) Composition of Wiener Functional . . 6.9 Stop Brownian Motion at Anticipative Exit Time......... Some Inequalities 7.1 Complex Hypercontractivity............................. 7.2 Meyer’s Inequality..................................... 7.3 Multiplier Theorem..................................... 7.4 Littlewood-Paley-Stein-Meyer Theory ................... 7.5 Meyer’s Inequalities Revisited ........................ 7.6 Interpolation Inequality............................... 7.7 Grothendieck Inequality................................ Convergence in Density 8.1 General Nonlinear Wiener Functional.................... 8.2 Weak Convergence....................................... 8.3 Representation of the Derivatives of the Density....... 8.4 Random Variables in the g-th Wiener Chaos.............. Contents xi 85 Uniform Estimation of Difference of Derivatives of Densities............................................ 292 8.6 Density Convergence of Higher Rank Hermite Polynomials 297 9. Local Time and (Self-) Intersection Local Time 311 9.1 Local Time of Brownian Motion........................... 311 9.2 Chaos Expansion of Self-intersection Local Time......... 314 93 Exponential Integrability............................... 320 9.4 Renormalization When d 3.............................. 324 9.5 L2-Modulus of Continuity of Local Time of Brownian Motion ..................................... 329 10. Stochastic Differential Equation 341 10.1 Existence, Uniqueness and Non-explosion ................ 341 10.2 Hörmander Theorem....................................... 347 10.3 Exponential Integrability............................... 364 10.4 Itö-Wiener Chaos Expansion ............................. 371 10.5 FKG Inequality and Variance Inequality.................. 373 10.6 Hypercontractivity, Spectral and Logarithmic Sobolev In- equality ..................................................... 376 10.7 Convergence to Density for Ergodic Diffusion............ 384 11. Numerical Approximation of Stochastic Differential Eequation 395 11.1 Lp-Convergence Rate..................................... 395 11.2 Convergence in and Convergence in Density.............. 403 11.3 Weak Convergence Rate................................... 417 11.4 Wong-Zakai Approximation................................ 421 Appendix A Appendix 427 A.l Some Elementary Results from Analysis................... 427 A. 2 Martingales............................................. 439 Bibliography 453 Index 467
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isbn	9789813142176
language	English
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spelling	Hu, Yaozhong Verfasser (DE-588)171537858 aut Analysis on Gaussian spaces Yaozhong Hu, University of Kansas, USA New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2017] © 2017 xi, 470 Seiten txt rdacontent n rdamedia nc rdacarrier Maßtheorie (DE-588)4074626-4 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Gauß-Maß (DE-588)4156113-2 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s Gauß-Maß (DE-588)4156113-2 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029258635&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Hu, Yaozhong Analysis on Gaussian spaces Maßtheorie (DE-588)4074626-4 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Gauß-Maß (DE-588)4156113-2 gnd
subject_GND	(DE-588)4074626-4 (DE-588)4064324-4 (DE-588)4156113-2
title	Analysis on Gaussian spaces
title_auth	Analysis on Gaussian spaces
title_exact_search	Analysis on Gaussian spaces
title_full	Analysis on Gaussian spaces Yaozhong Hu, University of Kansas, USA
title_fullStr	Analysis on Gaussian spaces Yaozhong Hu, University of Kansas, USA
title_full_unstemmed	Analysis on Gaussian spaces Yaozhong Hu, University of Kansas, USA
title_short	Analysis on Gaussian spaces
title_sort	analysis on gaussian spaces
topic	Maßtheorie (DE-588)4074626-4 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Gauß-Maß (DE-588)4156113-2 gnd
topic_facet	Maßtheorie Wahrscheinlichkeitsrechnung Gauß-Maß
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029258635&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT huyaozhong analysisongaussianspaces

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