Stochastic calculus of variations: for jump processes
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2023]
|
| Edition: | 3rd edition |
| Series: | De Gruyter Studies in Mathematics
volume 54 |
| Subjects: | |
| Online Access: | https://www.degruyter.com/isbn/9783110675283 Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XIII, 360 Seiten Illustrationen 24 cm x 17 cm, 751 g |
| ISBN: | 9783110675283 3110675285 |
Staff View
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| 100 | 1 | |a Ishikawa, Yasushi |d 1959- |e Verfasser |0 (DE-588)1036467341 |4 aut | |
| 245 | 1 | 0 | |a Stochastic calculus of variations |b for jump processes |c Yasushi Ishikawa |
| 250 | |a 3rd edition | ||
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2023] | |
| 300 | |a XIII, 360 Seiten |b Illustrationen |c 24 cm x 17 cm, 751 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter Studies in Mathematics |v volume 54 | |
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| 653 | |a Stochastische partielle Differentialgleichung | ||
| 653 | |a Malliavin-Kalkül | ||
| 653 | |a Stochastische Analysis | ||
| 653 | |a Stochastische Funktional-Differentialgleichung | ||
| 653 | |a Stochastische partielle Differentialgleichung; Malliavin-Kalkül; Stochastische Analysis; Stochastische Funktional-Differentialgleichung | ||
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Record in the Search Index
| _version_ | 1804185423198552064 |
|---|---|
| adam_text | CONTENTS
PREFACE
TO
THE
FIRST
EDITION
-
V
PREFACE
TO
THE
SECOND
EDITION
-
VII
PREFACE
TO
THE
THIRD
EDITION
-
IX
0
INTRODUCTION
-
1
1
1.1
1.1.1
1.1.2
1.1.3
1.2
1.2.1
1.2.2
1.2.3
1.2.4
1.3
1.3.1
LEVY
PROCESSES
AND
LTD
CALCULUS
-
5
POISSON
RANDOM
MEASURE
AND
LEVY
PROCESSES
-
5
LEVY
PROCESSES
-
5
EXAMPLES
OF
LEVY
PROCESSES
-
9
THE
STOCHASTIC
INTEGRAL
FOR
A
FINITE
VARIATION
PROCESS
AND
RELATED
TOPICS
-
14
BASIC
MATERIAL
FOR
SDES
WITH
JUMPS
-
16
MARTINGALES
AND
SEMIMARTINGALES
-
17
STOCHASTIC
INTEGRAL
WITH
RESPECT
TO
SEMIMARTINGALES
-
19
KUNITA-WATANABE
INEQUALITIES
-
28
DOLEANS-DADE
EXPONENTIAL
AND
GIRSANOV
TRANSFORMATION
-
31
LTD
PROCESSES
WITH
JUMPS
-
35
PURE
JUMP
TYPE
SDE
-
40
2
2.1
2.1.1
2.1.2
2.1.3
2.2
2.2.1
2.2.2
2.2.3
2.3
2.3.1
2.3.2
2.3.3
2.4
2.4.1
PERTURBATIONS
AND
PROPERTIES
OF
THE
PROBABILITY
LAW
-
47
INTEGRATION-BY-PARTS
ON
POISSON
SPACE
-
47
BISMUT
S
METHOD
-
50
PICARD
S
METHOD
-
61
SOME
PREVIOUS
METHODS
-
67
METHODS
OF
FINDING
THE
ASYMPTOTIC
BOUNDS
(I)
-
77
MARKOV
CHAIN
APPROXIMATION
-
78
PROOF
OF
THEOREM
2.3
-
82
PROOF
OF
LEMMAS
-
89
METHODS
OF
FINDING
THE
ASYMPTOTIC
BOUNDS
(II)
-
101
POLYGONAL
GEOMETRY
-
101
PROOF
OF
THEOREM
2.4
-
102
EXAMPLE
OF
THEOREM
2.4
-
EASY
CASES
-
112
SUMMARY
OF
SHORT-TIME
ASYMPTOTIC
BOUNDS
-
120
CASE
THAT
P{DZ)
IS
ABSOLUTELY
CONTINUOUS
WITH
RESPECT
TO
THE
M-DIMENSIONAL
LEBESGUE
MEASURE
DZ
-
120
2.4.2
2.5
2.5.1
CASE
THAT
P(DZ)
IS
SINGULAR
WITH
RESPECT
TO
DZ
-
121
AUXILIARY
TOPICS
-
123
MARCUS
CANONICAL
PROCESSES
-
124
XII
-
CONTENTS
2.5.2
2.5.3
2.5.4
ABSOLUTE
CONTINUITY
OF
THE
INFINITELY
DIVISIBLE
LAWS
-
126
CHAIN
MOVEMENT
APPROXIMATION
-
132
SUPPORT
THEOREM
FOR
CANONICAL
PROCESSES
-
142
3
3.1
3.1.1
3.1.2
3.2
3.2.1
3.2.2
3.2.3
3.3
3.3.1
3.3.2
3.3.3
3.4
3.5
3.5.1
3.5.2
3.6
3.6.1
3.6.2
3.6.3
3.6.4
3.6.5
3.7
ANALYSIS
OF
WIENER-POISSON
FUNCTIONALS
-
146
CALCULUS
OF
FUNCTIONALS
ON
THE
WIENER
SPACE
-
146
DEFINITION
OF
THE
MALLIAVIN-SHIGEKAWA
DERIVATIVE
D
T
-
148
ADJOINT
OPERATOR
8
=
D*
-
153
CALCULUS
OF
FUNCTIONALS
ON
THE
POISSON
SPACE
-
155
ONE-DIMENSIONAL
CASE
-
155
MULTIDIMENSIONAL
CASE
-
159
CHARACTERIZATION
OF
THE
POISSON
SPACE
-
162
SOBOLEV
SPACE
FOR
FUNCTIONALS
ON
THE
WIENER-POISSON
SPACE
-
166
THE
WIENER
SPACE
-
167
THE
POISSON
SPACE
-
169
THE
WIENER-POISSON
SPACE
-
191
RELATION
WITH
THE
MALLIAVIN
OPERATOR
-
204
COMPOSITION
ON
THE
WIENER-POISSON
SPACE
(I)
-
GENERAL
THEORY
-
206
COMPOSITION
WITH
AN
ELEMENT
IN
S
-
206
SUFFICIENT
CONDITION
FOR
THE
COMPOSITION
-
216
SMOOTHNESS
OF
THE
DENSITY
FOR
ITO
PROCESSES
-
223
PRELIMINARIES
-
223
BIG
PERTURBATIONS
-
231
CONCATENATION
(I)
-
235
CONCATENATION
(II)
-
THE
CASE
THAT
(D)
MAY
FAIL
-
238
MORE
ON
THE
DENSITY
-
244
COMPOSITION
ON
THE
WIENER-POISSON
SPACE
(II)
-
ITO
PROCESSES
-
261
4
4.1
4.1.1
4.1.2
4.1.3
4.2
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5
APPLICATIONS
-
265
ASYMPTOTIC
EXPANSION
OF
THE
SDE
-
265
ANALYSIS
ON
THE
STOCHASTIC
MODEL
-
268
ASYMPTOTIC
EXPANSION
OF
THE
DENSITY
-
291
EXAMPLES
OF
ASYMPTOTIC
EXPANSIONS
-
295
OPTIMAL
CONSUMPTION
PROBLEM
-
301
SETTING
OF
THE
OPTIMAL
CONSUMPTION
-
302
VISCOSITY
SOLUTIONS
-
305
REGULARITY
OF
SOLUTIONS
-
324
OPTIMAL
CONSUMPTION
-
328
HISTORICAL
SKETCH
-
331
A
A.1
APPENDIX
-
335
NOTES
AND
TRIVIAL
MATTERS
-
335
CONTENTS
-
XIII
A.1.1
A.1
.2
A.1
.3
NOTES
-
335
RAMSEY
THEORY
-
339
A
SMALL
APPLICATION
TO
NEURAL
CELL
THEORY
-
340
BIBLIOGRAPHY
-
347
LIST
OF
SYMBOLS
-
357
INDEX
-
359
|
| adam_txt |
CONTENTS
PREFACE
TO
THE
FIRST
EDITION
-
V
PREFACE
TO
THE
SECOND
EDITION
-
VII
PREFACE
TO
THE
THIRD
EDITION
-
IX
0
INTRODUCTION
-
1
1
1.1
1.1.1
1.1.2
1.1.3
1.2
1.2.1
1.2.2
1.2.3
1.2.4
1.3
1.3.1
LEVY
PROCESSES
AND
LTD
CALCULUS
-
5
POISSON
RANDOM
MEASURE
AND
LEVY
PROCESSES
-
5
LEVY
PROCESSES
-
5
EXAMPLES
OF
LEVY
PROCESSES
-
9
THE
STOCHASTIC
INTEGRAL
FOR
A
FINITE
VARIATION
PROCESS
AND
RELATED
TOPICS
-
14
BASIC
MATERIAL
FOR
SDES
WITH
JUMPS
-
16
MARTINGALES
AND
SEMIMARTINGALES
-
17
STOCHASTIC
INTEGRAL
WITH
RESPECT
TO
SEMIMARTINGALES
-
19
KUNITA-WATANABE
INEQUALITIES
-
28
DOLEANS-DADE
EXPONENTIAL
AND
GIRSANOV
TRANSFORMATION
-
31
LTD
PROCESSES
WITH
JUMPS
-
35
PURE
JUMP
TYPE
SDE
-
40
2
2.1
2.1.1
2.1.2
2.1.3
2.2
2.2.1
2.2.2
2.2.3
2.3
2.3.1
2.3.2
2.3.3
2.4
2.4.1
PERTURBATIONS
AND
PROPERTIES
OF
THE
PROBABILITY
LAW
-
47
INTEGRATION-BY-PARTS
ON
POISSON
SPACE
-
47
BISMUT
'
S
METHOD
-
50
PICARD
'
S
METHOD
-
61
SOME
PREVIOUS
METHODS
-
67
METHODS
OF
FINDING
THE
ASYMPTOTIC
BOUNDS
(I)
-
77
MARKOV
CHAIN
APPROXIMATION
-
78
PROOF
OF
THEOREM
2.3
-
82
PROOF
OF
LEMMAS
-
89
METHODS
OF
FINDING
THE
ASYMPTOTIC
BOUNDS
(II)
-
101
POLYGONAL
GEOMETRY
-
101
PROOF
OF
THEOREM
2.4
-
102
EXAMPLE
OF
THEOREM
2.4
-
EASY
CASES
-
112
SUMMARY
OF
SHORT-TIME
ASYMPTOTIC
BOUNDS
-
120
CASE
THAT
P{DZ)
IS
ABSOLUTELY
CONTINUOUS
WITH
RESPECT
TO
THE
M-DIMENSIONAL
LEBESGUE
MEASURE
DZ
-
120
2.4.2
2.5
2.5.1
CASE
THAT
P(DZ)
IS
SINGULAR
WITH
RESPECT
TO
DZ
-
121
AUXILIARY
TOPICS
-
123
MARCUS
'
CANONICAL
PROCESSES
-
124
XII
-
CONTENTS
2.5.2
2.5.3
2.5.4
ABSOLUTE
CONTINUITY
OF
THE
INFINITELY
DIVISIBLE
LAWS
-
126
CHAIN
MOVEMENT
APPROXIMATION
-
132
SUPPORT
THEOREM
FOR
CANONICAL
PROCESSES
-
142
3
3.1
3.1.1
3.1.2
3.2
3.2.1
3.2.2
3.2.3
3.3
3.3.1
3.3.2
3.3.3
3.4
3.5
3.5.1
3.5.2
3.6
3.6.1
3.6.2
3.6.3
3.6.4
3.6.5
3.7
ANALYSIS
OF
WIENER-POISSON
FUNCTIONALS
-
146
CALCULUS
OF
FUNCTIONALS
ON
THE
WIENER
SPACE
-
146
DEFINITION
OF
THE
MALLIAVIN-SHIGEKAWA
DERIVATIVE
D
T
-
148
ADJOINT
OPERATOR
8
=
D*
-
153
CALCULUS
OF
FUNCTIONALS
ON
THE
POISSON
SPACE
-
155
ONE-DIMENSIONAL
CASE
-
155
MULTIDIMENSIONAL
CASE
-
159
CHARACTERIZATION
OF
THE
POISSON
SPACE
-
162
SOBOLEV
SPACE
FOR
FUNCTIONALS
ON
THE
WIENER-POISSON
SPACE
-
166
THE
WIENER
SPACE
-
167
THE
POISSON
SPACE
-
169
THE
WIENER-POISSON
SPACE
-
191
RELATION
WITH
THE
MALLIAVIN
OPERATOR
-
204
COMPOSITION
ON
THE
WIENER-POISSON
SPACE
(I)
-
GENERAL
THEORY
-
206
COMPOSITION
WITH
AN
ELEMENT
IN
S
'
-
206
SUFFICIENT
CONDITION
FOR
THE
COMPOSITION
-
216
SMOOTHNESS
OF
THE
DENSITY
FOR
ITO
PROCESSES
-
223
PRELIMINARIES
-
223
BIG
PERTURBATIONS
-
231
CONCATENATION
(I)
-
235
CONCATENATION
(II)
-
THE
CASE
THAT
(D)
MAY
FAIL
-
238
MORE
ON
THE
DENSITY
-
244
COMPOSITION
ON
THE
WIENER-POISSON
SPACE
(II)
-
ITO
PROCESSES
-
261
4
4.1
4.1.1
4.1.2
4.1.3
4.2
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5
APPLICATIONS
-
265
ASYMPTOTIC
EXPANSION
OF
THE
SDE
-
265
ANALYSIS
ON
THE
STOCHASTIC
MODEL
-
268
ASYMPTOTIC
EXPANSION
OF
THE
DENSITY
-
291
EXAMPLES
OF
ASYMPTOTIC
EXPANSIONS
-
295
OPTIMAL
CONSUMPTION
PROBLEM
-
301
SETTING
OF
THE
OPTIMAL
CONSUMPTION
-
302
VISCOSITY
SOLUTIONS
-
305
REGULARITY
OF
SOLUTIONS
-
324
OPTIMAL
CONSUMPTION
-
328
HISTORICAL
SKETCH
-
331
A
A.1
APPENDIX
-
335
NOTES
AND
TRIVIAL
MATTERS
-
335
CONTENTS
-
XIII
A.1.1
A.1
.2
A.1
.3
NOTES
-
335
RAMSEY
THEORY
-
339
A
SMALL
APPLICATION
TO
NEURAL
CELL
THEORY
-
340
BIBLIOGRAPHY
-
347
LIST
OF
SYMBOLS
-
357
INDEX
-
359 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Ishikawa, Yasushi 1959- |
| author_GND | (DE-588)1036467341 |
| author_facet | Ishikawa, Yasushi 1959- |
| author_role | aut |
| author_sort | Ishikawa, Yasushi 1959- |
| author_variant | y i yi |
| building | Verbundindex |
| bvnumber | BV049088502 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)1392144487 (DE-599)DNB1283839342 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 3rd edition |
| format | Book |
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| id | DE-604.BV049088502 |
| illustrated | Illustrated |
| index_date | 2024-07-03T22:29:16Z |
| indexdate | 2024-07-10T09:55:00Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110675283 3110675285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034350276 |
| oclc_num | 1392144487 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | XIII, 360 Seiten Illustrationen 24 cm x 17 cm, 751 g |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter Studies in Mathematics |
| series2 | De Gruyter Studies in Mathematics |
| spelling | Ishikawa, Yasushi 1959- Verfasser (DE-588)1036467341 aut Stochastic calculus of variations for jump processes Yasushi Ishikawa 3rd edition Berlin ; Boston De Gruyter [2023] XIII, 360 Seiten Illustrationen 24 cm x 17 cm, 751 g txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematics volume 54 Malliavin-Kalkül (DE-588)4242584-0 gnd rswk-swf Sprungprozess (DE-588)4427906-1 gnd rswk-swf Stochastische partielle Differentialgleichung Malliavin-Kalkül Stochastische Analysis Stochastische Funktional-Differentialgleichung Stochastische partielle Differentialgleichung; Malliavin-Kalkül; Stochastische Analysis; Stochastische Funktional-Differentialgleichung Sprungprozess (DE-588)4427906-1 s Malliavin-Kalkül (DE-588)4242584-0 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-067529-0 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-067532-0 Vorangegangen ist 9783110377767 De Gruyter Studies in Mathematics volume 54 (DE-604)BV000005407 54 X:MVB https://www.degruyter.com/isbn/9783110675283 B:DE-101 application/pdf https://d-nb.info/1283839342/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034350276&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20230319 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Ishikawa, Yasushi 1959- Stochastic calculus of variations for jump processes De Gruyter Studies in Mathematics Malliavin-Kalkül (DE-588)4242584-0 gnd Sprungprozess (DE-588)4427906-1 gnd |
| subject_GND | (DE-588)4242584-0 (DE-588)4427906-1 |
| title | Stochastic calculus of variations for jump processes |
| title_auth | Stochastic calculus of variations for jump processes |
| title_exact_search | Stochastic calculus of variations for jump processes |
| title_exact_search_txtP | Stochastic calculus of variations for jump processes |
| title_full | Stochastic calculus of variations for jump processes Yasushi Ishikawa |
| title_fullStr | Stochastic calculus of variations for jump processes Yasushi Ishikawa |
| title_full_unstemmed | Stochastic calculus of variations for jump processes Yasushi Ishikawa |
| title_short | Stochastic calculus of variations |
| title_sort | stochastic calculus of variations for jump processes |
| title_sub | for jump processes |
| topic | Malliavin-Kalkül (DE-588)4242584-0 gnd Sprungprozess (DE-588)4427906-1 gnd |
| topic_facet | Malliavin-Kalkül Sprungprozess |
| url | https://www.degruyter.com/isbn/9783110675283 https://d-nb.info/1283839342/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034350276&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT ishikawayasushi stochasticcalculusofvariationsforjumpprocesses AT walterdegruytergmbhcokg stochasticcalculusofvariationsforjumpprocesses |
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