Diffusion processes and their sample paths:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kon
Springer
1996
|
| Edition: | Reprint of the 1974 ed. |
| Series: | Grundlehren der mathematischen Wissenschaften
Vol. 125 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 306 - 312 |
| Physical Description: | XIV, 321 S. graph. Darst. |
| ISBN: | 3540606297 |
Staff View
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| 245 | 1 | 0 | |a Diffusion processes and their sample paths |c Kiosi Itô ; Henry P. McKean, Jr. |
| 250 | |a Reprint of the 1974 ed. | ||
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kon |b Springer |c 1996 | |
| 300 | |a XIV, 321 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v Vol. 125 | |
| 490 | 0 | |a Classics in mathematics | |
| 500 | |a Literaturverz. S. 306 - 312 | ||
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Record in the Search Index
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| adam_text |
Contents
page
Prerequisites
. 1
Chapter l. The standard BROWNian motion
. 5
l.t. The standard random walk
. 5
1.2.
Passage times for the standard random walk
. 7
1.3.
Hincin's proof of the
de Moivrk-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 Hausdorff-Besicovitch 1/2-dimensional measure
. 50
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
Ώ
. 94
3.7.
Generators
. . ■. 98
3.8.
Generators continued
. 100
3.9.
Stopped diffusion
. 102
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 ®'u = a,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.
KOLMOGOEOV'S test
.
1ÓÍ
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
. 176
5.6.
Killing times
. 179
5.7.
Feller's BROWNian motions
. 186
5.8.
Ikeda's example
. 188
5.9.
Time substitutions must come from local time integrals
. 190
5.1Ü.
Shunts
. 191
5.11.
Shunts with killing
.
I96
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
ană
the intervals of
[0,
-foo)
—
S
. 218
6.4.
A counter example:
t
and the intervals of
[0, + 00) — $. 220
6.5a
t
and downcrossings
. 222
6.5b
t
as Hausdorff measure
. 223
6.5c
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
.228
Chapter
7.
BROWNian motion in several dimensions
.232
7.1.
Diffusion in several dimensions
.232
7.2.
The standard BROWNian motion in several dimensions
.-233
7.3.
Wandering out to
00.236
page
7.4.
GREENian domains and Green functions
. 237
7.5.
Excessive functions
. 243
7.6.
Application to the spectrum of
Δ/2
. 245
7.7.
Potentials and hitting probabilities
. 247
7.8.
NEWTONian capacities
.
2S0
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
.
26I
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
BROWNÎan
motions
. 279
7.19.
Diffusions with BROWNian bitting 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.
® 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 |
| any_adam_object | 1 |
| author | Itō, Kiyoshi 1915-2008 McKean, Henry P. 1930-2024 |
| author_GND | (DE-588)119388073 (DE-588)130546275 |
| author_facet | Itō, Kiyoshi 1915-2008 McKean, Henry P. 1930-2024 |
| author_role | aut aut |
| author_sort | Itō, Kiyoshi 1915-2008 |
| author_variant | k i ki h p m hp hpm |
| building | Verbundindex |
| bvnumber | BV010511136 |
| classification_rvk | SK 820 |
| classification_tum | MAT 605f |
| ctrlnum | (OCoLC)758347631 (DE-599)BVBBV010511136 |
| dewey-full | 519.233 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.233 |
| dewey-search | 519.233 |
| dewey-sort | 3519.233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Reprint of the 1974 ed. |
| format | Book |
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| id | DE-604.BV010511136 |
| illustrated | Illustrated |
| indexdate | 2024-08-20T00:35:14Z |
| institution | BVB |
| isbn | 3540606297 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007006356 |
| oclc_num | 758347631 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-573 DE-739 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-573 DE-739 DE-188 |
| physical | XIV, 321 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften Classics in mathematics |
| spelling | Itō, Kiyoshi 1915-2008 Verfasser (DE-588)119388073 aut Diffusion processes and their sample paths Kiosi Itô ; Henry P. McKean, Jr. Reprint of the 1974 ed. Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kon Springer 1996 XIV, 321 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften Vol. 125 Classics in mathematics Literaturverz. S. 306 - 312 Mouvement brownien, Processus de ram Processus de diffusion ram mouvement brownien inriac processus diffusion inriac processus stochastique inriac temps local inriac échantillonnage inriac Stochastik (DE-588)4121729-9 gnd rswk-swf Differentialoperator (DE-588)4012251-7 gnd rswk-swf Theorie (DE-588)4059787-8 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Diffusion (DE-588)4012277-3 gnd rswk-swf Diffusion (DE-588)4012277-3 s Mathematik (DE-588)4037944-9 s Theorie (DE-588)4059787-8 s 1\p DE-604 Brownsche Bewegung (DE-588)4128328-4 s Diffusionsprozess (DE-588)4274463-5 s 2\p DE-604 3\p DE-604 Stochastik (DE-588)4121729-9 s 4\p DE-604 Differentialoperator (DE-588)4012251-7 s 5\p DE-604 Stochastischer Prozess (DE-588)4057630-9 s 6\p DE-604 McKean, Henry P. 1930-2024 Verfasser (DE-588)130546275 aut Grundlehren der mathematischen Wissenschaften Vol. 125 (DE-604)BV000000395 125 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007006356&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Itō, Kiyoshi 1915-2008 McKean, Henry P. 1930-2024 Diffusion processes and their sample paths Grundlehren der mathematischen Wissenschaften Mouvement brownien, Processus de ram Processus de diffusion ram mouvement brownien inriac processus diffusion inriac processus stochastique inriac temps local inriac échantillonnage inriac Stochastik (DE-588)4121729-9 gnd Differentialoperator (DE-588)4012251-7 gnd Theorie (DE-588)4059787-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Mathematik (DE-588)4037944-9 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Diffusionsprozess (DE-588)4274463-5 gnd Diffusion (DE-588)4012277-3 gnd |
| subject_GND | (DE-588)4121729-9 (DE-588)4012251-7 (DE-588)4059787-8 (DE-588)4057630-9 (DE-588)4037944-9 (DE-588)4128328-4 (DE-588)4274463-5 (DE-588)4012277-3 |
| 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 Kiosi Itô ; Henry P. McKean, Jr. |
| title_fullStr | Diffusion processes and their sample paths Kiosi Itô ; Henry P. McKean, Jr. |
| title_full_unstemmed | Diffusion processes and their sample paths Kiosi Itô ; Henry P. McKean, Jr. |
| title_short | Diffusion processes and their sample paths |
| title_sort | diffusion processes and their sample paths |
| topic | Mouvement brownien, Processus de ram Processus de diffusion ram mouvement brownien inriac processus diffusion inriac processus stochastique inriac temps local inriac échantillonnage inriac Stochastik (DE-588)4121729-9 gnd Differentialoperator (DE-588)4012251-7 gnd Theorie (DE-588)4059787-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Mathematik (DE-588)4037944-9 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Diffusionsprozess (DE-588)4274463-5 gnd Diffusion (DE-588)4012277-3 gnd |
| topic_facet | Mouvement brownien, Processus de Processus de diffusion mouvement brownien processus diffusion processus stochastique temps local échantillonnage Stochastik Differentialoperator Theorie Stochastischer Prozess Mathematik Brownsche Bewegung Diffusionsprozess Diffusion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007006356&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 |