Verfügbarkeit: Diffusion processes and their sample paths

Diffusion processes and their sample paths:

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Bibliographische Detailangaben
Beteiligte Personen:	Itō, Kiyoshi 1915-2008 (VerfasserIn), McKean, Henry P. 1930-2024 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 1974
Ausgabe:	Second printing corrected
Schriftenreihe:	Die Grundlehren der mathematischen Wissenschaften Band 125
Schlagwörter:	Capacité Diffusion (physique) Diffusion Mesure Lévy Mouvement brownien Potentiel Riesz Processus Bessel Processus de diffusion Processus stochastiques Brownian movements Stochastic processes Differentialoperator Stochastik Stochastischer Prozess Theorie Mathematik Diffusionsprozess Brownsche Bewegung
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005991980&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XIV, 321 Seiten Illustrationen
ISBN:	3540033025 0387033025

Internformat

MARC


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Datensatz im Suchindex

DE-BY-TUM_call_number	0102 MAT 605f 2001 A 6461(1,1974)
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adam_text	Contents page Prerequisites 1 Chapter l. The standard BROWNian motion 5 1.1. The standard random walk 5 1.2. Passage times for the standard random walk 7 1.3. Hincin s proof of the de Moivre-Laplace limit theorem .... 10 1.4. The standard BROWNian motion 12 1.5. P. Levy s construction 19 1.6. Strict Markov character 22 1.7. Passage times for the standard BROWNian motion 25 Note 1: Homogeneous differential processes with increasing paths 31 1.8. Kolmogorov s test and the law of the iterated logarithm .... 33 1.9. P. Levy s Holder condition 36 1.10. Approximating the BROWNian motion by a random walk .... 38 Chapter 2. BROWNian local times 40 2.1. The reflecting BROWNian motion 40 2.2. P. Levy s local time 42 2.3. Elastic BROWNian motion 45 2.4. t+ and down-crossings 48 2.5. t+ as Haxjsdorff-Besicovitch 1/2-dimensional measure SO Note 1: Submartingales 52 Note 2: Hausdorff measure and dimension 53 2.6. Kac s formula for BROWNian functionals 54 2.7. Bessel processes 59 2.8. Standard BROWNian local time 63 2.9. BROWNian excursions 75 2.10. Application of the Bessel process to BROWNian excursions . . . 79 2.11. A time substitution 81 Chapter 3. The general 1-dimensional diffusion 83 3.1. Definition 83 3.2. Markov times 86 3.3. Matching numbers 89 3.4. Singular points 91 3.5. Decomposing the general diffusion into simple pieces 92 3.6. Green operators and the space D 94 3.7. Generators . . • 98 3.8. Generators continued * 100 3.9. Stopped diffusion 102 Contents XIII page Chapter 4. Generators 105 4.1. A general view 105 4.2. © as local differential operator: conservative non-singular case . . Ill 4.3. © as local differential operator: general non-singular case .... 116 4.4. A second proof 119 4.5. © at an isolated singular point 125 4.6. Solving ©*« = (X u 128 4.7. © as global differential operator: non-singular case 135 4.8. © on the shunts 136 4.9. © as global differential operator: singular case 142 4.10. Passage times 144 Note 1: Differential processes with increasing paths 146 4.11. Eigen-differential expansions for Green functions and transition densities 149 4.12. Kolmogorov s test 161 Chapter 5. Time changes and killing 164 5.1. Construction of sample paths: a general view 164 5.2. Time changes: Q = R1 167 5.3. Time changes: Q = [0, +00) 171 5.4. Local times 174 5.5. Subordination and chain rule I76 5.6. Killing times 179 5.7. Feller s BROwNian motions 186 5.8. Ikeda s example 18S 5.9. Time substitutions must come from local time integrals 190 5.1U. Shunts 191 5.11. Shunts with killing 196 5.12. Creation of mass 200 5.13. A parabolic equation 201 5.14. Explosions 206 5.15. A non-linear parabolic equation 209 Chapter 6. Local and inverse local times 212 6.1. Local and inverse local times 212 6.2. Levy measures 214 6.3. t and the intervals of [0, + 00) — 3 218 6.4. A counter example: t and the intervals of [0, +00) — g 220 6.5 a t and downcrossings 222 6.5b t as Hausdorff measure 223 6.5 c t as diffusion 223 6.5d Excursions 223 6.6. Dimension numbers 224 6.7. Comparison tests 225 Note 1: Dimension numbers and fractional dimensional capacities 227 6.8. An individual ergodic theorem 22S Chapter 7. BROWNian motion in several dimensions 232 7.1. Diffusion in several dimensions 232 7.2. The standard BROWKian motion in several dimensions 233 7.3. Wandering out to 00 236 XIV Contents page 7.4. GREENian domains and Gkeen functions 237 7.5. Excessive functions 243 7.6. Application to the spectrum of Aji 245 7.7- Potentials and hitting probabilities 247 7.8. NEWTONian capacities 250 7.9. Gauss s quadratic form 253 7.10. Wiener s test 255 7.11. Applications of Wiener s test 257 7.12. Dirichlet problem 261 7.13. Neumann problem 264 7.14. Space-time BROWNian motion 266 7.15. Spherical BROWNian motion and skew products 269 7.16. Spinning 274 7.17- An individual ergodic theorem for the standard 2-dimensional BROWNian motion 277 7.18. Covering BROwNfan motions 279 7.19. Diffusions with BROWNian hitting probabilities 283 7.20. Right-continuous paths 286 7.21. Riesz potentials 288 Chapter 8. A general view of diffusion in several dimensions . . . 291 8.1. Similar diffusions 291 8.2. 3 as differential operator 293 8.3- Time substitutions 295 8.4. Potentials 296 8.5. Boundaries 299 8.6. Elliptic operators 302 8.7. Feller s little boundary and tail algebras 303 Bibliography 306 List of notations 313 Index 315
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series	Die Grundlehren der mathematischen Wissenschaften
series2	Die Grundlehren der mathematischen Wissenschaften
spellingShingle	Itō, Kiyoshi 1915-2008 McKean, Henry P. 1930-2024 Diffusion processes and their sample paths Die Grundlehren der mathematischen Wissenschaften Capacité Jussieu Diffusion (physique) ram Diffusion Jussieu Mesure Lévy Jussieu Mouvement brownien Jussieu Mouvement brownien ram Potentiel Riesz Jussieu Processus Bessel Jussieu Processus de diffusion ram Processus stochastiques ram Brownian movements Diffusion Stochastic processes Differentialoperator (DE-588)4012251-7 gnd Stochastik (DE-588)4121729-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Theorie (DE-588)4059787-8 gnd Diffusion (DE-588)4012277-3 gnd Mathematik (DE-588)4037944-9 gnd Diffusionsprozess (DE-588)4274463-5 gnd Brownsche Bewegung (DE-588)4128328-4 gnd
subject_GND	(DE-588)4012251-7 (DE-588)4121729-9 (DE-588)4057630-9 (DE-588)4059787-8 (DE-588)4012277-3 (DE-588)4037944-9 (DE-588)4274463-5 (DE-588)4128328-4
title	Diffusion processes and their sample paths
title_auth	Diffusion processes and their sample paths
title_exact_search	Diffusion processes and their sample paths
title_full	Diffusion processes and their sample paths K. Itô ; H. P. McKean
title_fullStr	Diffusion processes and their sample paths K. Itô ; H. P. McKean
title_full_unstemmed	Diffusion processes and their sample paths K. Itô ; H. P. McKean
title_short	Diffusion processes and their sample paths
title_sort	diffusion processes and their sample paths
topic	Capacité Jussieu Diffusion (physique) ram Diffusion Jussieu Mesure Lévy Jussieu Mouvement brownien Jussieu Mouvement brownien ram Potentiel Riesz Jussieu Processus Bessel Jussieu Processus de diffusion ram Processus stochastiques ram Brownian movements Diffusion Stochastic processes Differentialoperator (DE-588)4012251-7 gnd Stochastik (DE-588)4121729-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Theorie (DE-588)4059787-8 gnd Diffusion (DE-588)4012277-3 gnd Mathematik (DE-588)4037944-9 gnd Diffusionsprozess (DE-588)4274463-5 gnd Brownsche Bewegung (DE-588)4128328-4 gnd
topic_facet	Capacité Diffusion (physique) Diffusion Mesure Lévy Mouvement brownien Potentiel Riesz Processus Bessel Processus de diffusion Processus stochastiques Brownian movements Stochastic processes Differentialoperator Stochastik Stochastischer Prozess Theorie Mathematik Diffusionsprozess Brownsche Bewegung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005991980&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000395
work_keys_str_mv	AT itokiyoshi diffusionprocessesandtheirsamplepaths AT mckeanhenryp diffusionprocessesandtheirsamplepaths

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