Geometric stochastic calculus:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Bonn
Univ.
2002
|
| Series: | Vorlesungsreihe / Rheinische Friedrich-Wilhelms-Universität Bonn, Sonderforschungsbereich 256 Nichtlineare Partielle Differentialgleichungen
45 |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Rudolph-Lipschitz-Vorlesung |
| Physical Description: | 59 S. |
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MARC
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| 100 | 1 | |a Malliavin, Paul |d 1925-2010 |e Verfasser |0 (DE-588)115728023 |4 aut | |
| 245 | 1 | 0 | |a Geometric stochastic calculus |c Paul Malliavin |
| 264 | 1 | |a Bonn |b Univ. |c 2002 | |
| 300 | |a 59 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Vorlesungsreihe / Rheinische Friedrich-Wilhelms-Universität Bonn, Sonderforschungsbereich 256 Nichtlineare Partielle Differentialgleichungen |v 45 | |
| 500 | |a Rudolph-Lipschitz-Vorlesung | ||
| 810 | 2 | |a Rheinische Friedrich-Wilhelms-Universität Bonn, Sonderforschungsbereich 256 Nichtlineare Partielle Differentialgleichungen |t Vorlesungsreihe |v 45 |w (DE-604)BV005631830 |9 45 | |
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Record in the Search Index
| _version_ | 1807682919195475968 |
|---|---|
| adam_text |
CONTENTS
1
UNIVERSAL
PROBABILITY
SPACE
1
1.1
WIENER
MEASURE
ASSOCIATED
TO
AN
ELLIPTIC
OPERATOR
.
1
1.2
PROBLEM
OF
UNIVERSALITY
.
2
1.3
RESOLUTION
OF
THE
UNIVERSALITY
PROBLEM
FOR
RIEMANNIAN
MANIFOLDS
2
1.4
THE
BROWNIAN
MOTIONS
ON
R
D
.
3
1.5
SOLUTION
OF
THE
UNIVERSALITY
PROBLEM
BY
THE
ITO
MAP
.
4
1.6
UNIVERSAL
MODEL
FOR
THE
BROWNIAN
MOTION
ON
A
RIEMANNIAN
MANIFOLD
.
6
2
DIFFERENTIAL
CALCULUS
8
2.1
CAMERON
-
MARTIN
THEOREM
.
8
2.2
NOTION
OF
DIVERGENCE
.
12
2.3
SHIGEKAWA
IDENTITY
.
13
2.4
METHOD
OF
PROOF
OF
SHIGEKAWA
.
14
3
STOCHASTIC
INTEGRALS
15
3.1
MAIN
OBJECTIVES
.
15
3.2
PARTIAL
DERIVATIVE
.
15
3.3
WIENER
STOCHASTIC
INTEGRAL
.
16
3.4
AMPLIFICATION:
ITO
STOCHASTIC
INTEGRAL
.
18
3.5
ITO
THEOREM
OF
CONSERVATION
OF
ENERGY
.
18
3.6
SEMI
MARTINGALE
.
19
3.7
STRUCTURE
THEOREM
.
19
3.8
CLARK-OCONE
FORMULA
.
20
4
STOCHASTIC
CALCULUS
22
4.1
ITO
SDE
VERSUS
STRATONOVITCH
SDE
.
22
4.2
CALCULUS
OF
VARIATION
ON
THE
HORIZONTAL
CONTROL
MAP
ON
THE
BUNDLE
OF
FRAMES
.
23
4.2.1
CURVATURE
TENSOR
OF
RIEMANN
AS
AN
OBSTRUCTION
OF
THE
FLATNESS
.
24
CONTENTS
1
4.3
STOCHASTIC
CALCULUS
OF
VARIATION
UPON
THE
STARTING
POINT
.
25
4.4
STOCHASTIC
CALCULUS
OF
VARIATION
OF
THE
PATH
SPACE
.
25
4.5
FORMULA
OF
INTEGRATION
BY
PART
ON
P
RNO
(M)
.
27
4.6
CAMERON
-
MARTIN
SPACE
.
27
4.7
CLARK-OCONE-BISMUT
FORMULA
.
28
5
STRUCTURAL
EQUATION
29
5.1
STRUCTURAL
EQUATION
.
30
5.2
MAIN
THEOREM:
.
30
5.3
LEVI-CIVITA
CONNECTION
.
33
5.4
WEITZENBBCK
IDENTITY
.
34
6
ANTICIPATIVE
STOCHASTIC
INTEGRAL
35
6.1
ANTICIPATIVE
INTEGRAL
AS
DIVERGENCE
.
35
6.2
CONSTRUCTION
BY
APPROXIMATION
BY
FINITE
SUMS
.
35
6.3
MODIFIED
STRATONOVITCH
AND
MODIFIED
NPZ
INTEGRAL
ASSOCIATED
TO
TANGENT
PROCESS
.
39
7
FRAME
BUNDLE
AND
WEITZENBOCK
FORMULA
42
7.1
COVARIANT
DERIVATIVE
.
44
7.2
METHODOLOGY
OF
PROOF
OF
STRUCTURE
THEOREM
.
46
7.3
ORNSTEIN
-
UHLENBECK
PROCESS
ON
P
TNO
(M)
.
47
8
PASSAGE
FROM
PATH
TO
THE
LOOP
49
8.1
DOOB
'
S
H-THEORY
.
49
8.2
STOCHASTIC
CALCULUS
OF
VARIATION
.
50
8.3
SMOOTHNESS
OF
LAW
.
51
8.4
COVERING
VECTOR
FIELD
.
51
8.5
THEOREM
OF
CONTINUOUS
DESINTEGRATION
.
52
8.6
QUASI
SURE
ANALYSIS
.
53
8.7
THEOREM
OF
TIGHTNESS
OF
CAPACITY
.
53
8.8
THE
WATANABE
DISTRIBUTION
.
54
8.9
PROOF
OF
THE
CONTINUOUS
DESINTEGRATION
ALONG
A
NON
DEGENER
ATED
MAP
.
55
8.10
REDEFINITION
.
56
8.11
PRINCIPLE
OF
DESCENT
.
57
8.12
APPLICATION
OF
THE
PRINCIPLE
OF
DESCENT
TO
A
FORMULA
OF
INTEGRA
TION
BY
PART
ON
LOOP
SPACE
.
57 |
| any_adam_object | 1 |
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| id | DE-604.BV016476560 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-18T00:26:11Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010186312 |
| oclc_num | 52684699 |
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| physical | 59 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Univ. |
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| series2 | Vorlesungsreihe / Rheinische Friedrich-Wilhelms-Universität Bonn, Sonderforschungsbereich 256 Nichtlineare Partielle Differentialgleichungen |
| spelling | Malliavin, Paul 1925-2010 Verfasser (DE-588)115728023 aut Geometric stochastic calculus Paul Malliavin Bonn Univ. 2002 59 S. txt rdacontent n rdamedia nc rdacarrier Vorlesungsreihe / Rheinische Friedrich-Wilhelms-Universität Bonn, Sonderforschungsbereich 256 Nichtlineare Partielle Differentialgleichungen 45 Rudolph-Lipschitz-Vorlesung Rheinische Friedrich-Wilhelms-Universität Bonn, Sonderforschungsbereich 256 Nichtlineare Partielle Differentialgleichungen Vorlesungsreihe 45 (DE-604)BV005631830 45 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010186312&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Malliavin, Paul 1925-2010 Geometric stochastic calculus |
| title | Geometric stochastic calculus |
| title_auth | Geometric stochastic calculus |
| title_exact_search | Geometric stochastic calculus |
| title_full | Geometric stochastic calculus Paul Malliavin |
| title_fullStr | Geometric stochastic calculus Paul Malliavin |
| title_full_unstemmed | Geometric stochastic calculus Paul Malliavin |
| title_short | Geometric stochastic calculus |
| title_sort | geometric stochastic calculus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010186312&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005631830 |
| work_keys_str_mv | AT malliavinpaul geometricstochasticcalculus |