Feynman-Kac-type theorems and Gibbs measures on path space:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
[2020-2020]
|
| Ausgabe: | 2nd edition |
| Schriftenreihe: | De Gruyter Studies in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 2 Bände |
Internformat
MARC
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| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Lőrinczi, József |d 1966- |e Verfasser |0 (DE-588)173059767 |4 aut | |
| 245 | 1 | 0 | |a Feynman-Kac-type theorems and Gibbs measures on path space |c József Lőrinczi, Fumio Hiroshima, and Volker Betz |
| 250 | |a 2nd edition | ||
| 264 | 1 | |a Berlin |b De Gruyter |c [2020-2020] | |
| 300 | |a 2 Bände | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter Studies in Mathematics | |
| 650 | 0 | 7 | |a Selbstadjungierter Operator |0 (DE-588)4180810-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Feynman-Kac-Formel |0 (DE-588)4820124-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gibbs-Maß |0 (DE-588)4157328-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Pfadintegral |0 (DE-588)4173973-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastische Analysis |0 (DE-588)4132272-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |2 gnd |9 rswk-swf |
| 653 | |a Feynman-Kac-TypeTheorems; Gibbs Measures; Quantum Field Theory; Brownian Motion | ||
| 689 | 0 | 0 | |a Selbstadjungierter Operator |0 (DE-588)4180810-1 |D s |
| 689 | 0 | 1 | |a Feynman-Kac-Formel |0 (DE-588)4820124-8 |D s |
| 689 | 0 | 2 | |a Pfadintegral |0 (DE-588)4173973-5 |D s |
| 689 | 0 | 3 | |a Gibbs-Maß |0 (DE-588)4157328-6 |D s |
| 689 | 0 | 4 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |D s |
| 689 | 0 | 5 | |a Stochastische Analysis |0 (DE-588)4132272-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Hiroshima, Fumio |e Verfasser |0 (DE-588)1016708270 |4 aut | |
| 700 | 1 | |a Betz, Volker |d 1972- |e Verfasser |0 (DE-588)123809568 |4 aut | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028333863&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-028333863 | ||
Datensatz im Suchindex
| _version_ | 1804175201041121280 |
|---|---|
| adam_text | CONTENTS
PREFACE
TO
THE
SECOND
EDITION
*
IX
PREFACE
TO
THE
FIRST
EDITION
*
XI
1
HEURISTICS
AND
HISTORY
*
1
1.1
FEYNMAN
PATH
INTEGRALS
AND
FEYNMAN-KAC
FORMULAE
*
1
1.2
PLAN
AND
SCOPE
OF
THE
SECOND
EDITION
*
5
2
BROWNIAN
MOTION
*
9
2.1
CONCEPTS
AND
FACTS
OF
GENERAL
MEASURE
THEORY
AND
PROBABILITY
*
9
2.1.1
ELEMENTS
OF
GENERAL
MEASURE
THEORY
*
9
2.1.2
PROBABILITY
MEASURES
AND
LIMIT
THEOREMS
*
16
2.1.3
RANDOM
VARIABLES
*
29
2.1.4
CONDITIONAL
EXPECTATION
AND
REGULAR
CONDITIONAL
PROBABILITY
MEASURES
*
38
2.2
RANDOM
PROCESSES
------
45
2.2.1
BASIC
CONCEPTS
AND
FACTS
*
45
2.2.2
MARTINGALE
PROPERTIES
-----
50
2.2.3
STOPPING
TIMES
AND
OPTIONAL
SAMPLING
*
53
2.2.4
MARKOV
PROPERTIES
-----
67
2.2.5
FELLER
TRANSITION
KERNELS
AND
GENERATORS
*
72
2.2.6
INVARIANT
MEASURES
*
74
2.3
BROWNIAN
MOTION
AND
WIENER
MEASURE
*
77
2.3.1
CONSTRUCTION
OF
BROWNIAN
MOTION
*
77
2.3.2
TWO-SIDED
BROWNIAN
MOTION
-----
84
2.3.3
CONDITIONAL
WIENER
MEASURE
*
88
2.3.4
MARTINGALE
PROPERTIES
OF
BROWNIAN
MOTION
*
89
2.3.5
MARKOV
PROPERTIES
OF
BROWNIAN
MOTION
*
92
2.3.6
LOCAL
PATH
PROPERTIES
OF
BROWNIAN
MOTION
*
97
2.3.7
GLOBAL
PATH
PROPERTIES
OF
BROWNIAN
MOTION
*
103
2.4
STOCHASTIC
CALCULUS
BASED
ON
BROWNIAN
MOTION
*
107
2.4.1
THE
CLASSICAL
INTEGRAL
AND
ITS
EXTENSIONS
*
107
2.4.2
STOCHASTIC
INTEGRALS
*
108
2.4.3
EXTENSION
OF
STOCHASTIC
INTEGRALS
*
115
2.4.4
LTD
FORMULA
-----
119
2.4.5
STOCHASTIC
DIFFERENTIAL
EQUATIONS
*
128
2.4.6
BROWNIAN
BRIDGE
*
134
2.4.7
WEAK
SOLUTION
AND
TIME
CHANGE
*
136
2.4.8
GIRSANOV
THEOREM
AND
CAMERON-MARTIN
FORMULA
*
140
VI
*
CONTENTS
3
L6VY
PROCESSES
*
143
3.1
LEVY
PROCESSES
AND
THE
LEVY-KHINTCHINE
FORMULA
*
143
3.1.1
INFINITELY
DIVISIBLE
RANDOM
VARIABLES
*
143
3.1.2
LEVY-KHINTCHINE
FORMULA
-----
149
3.1.3
LEVY
PROCESSES
*
154
3.1.4
MARTINGALE
PROPERTIES
OF
LEVY
PROCESSES
*
160
3.1.5
MARKOV
PROPERTIES
OF
LEVY
PROCESSES
*
161
3.2
SAMPLE
PATH
PROPERTIES
OF
LEVY
PROCESSES
*
165
3.2.1
CADLAG
VERSION
*
165
3.2.2
TWO-SIDED
LEVY
PROCESSES
*
169
3.3
RANDOM
MEASURES
AND
LEVY-LTD
DECOMPOSITION
-----
178
3.3.1
POISSON
RANDOM
MEASURES
*
178
3.3.2
LEVY-LTD
DECOMPOSITION
*
186
3.4
LTD
FORMULA
FOR
SEMIMARTINGALES
*
188
3.4.1
POINT
PROCESSES
*
188
3.4.2
LTD
FORMULA
FOR
SEMIMARTINGALES
*
194
3.5
EXPONENTIALS
OF
LEVY
PROCESSES
AND
RECURRENCE
PROPERTIES
*
201
3.5.1
EXPONENTIAL
FUNCTIONALS
OF
LEVY
PROCESSES
*
201
3.5.2
CAPACITARY
MEASURES
*
203
3.5.3
RECURRENCE
PROPERTIES
OF
LEVY
PROCESSES
*
204
3.6
SUBORDINATES
AND
BERNSTEIN
FUNCTIONS
*
206
3.6.1
SUBORDINATES
AND
SUBORDINATE
BROWNIAN
MOTION
-----
206
3.6.2
BERNSTEIN
FUNCTIONS
*
209
4
FEYNMAN-KAC
FORMULAE
*
217
4.1
SCHRODINGER
SEMIGROUPS
*
217
4.1.1
SCHRODINGER EQUATION
AND
PATH
INTEGRAL
SOLUTIONS
*
217
4.1.2
LINEAR
OPERATORS
AND
THEIR
SPECTRA
*
218
4.1.3
SPECTRAL
RESOLUTION
*
223
4.1.4
COMPACT
OPERATORS
AND
TRACE
IDEALS
*
227
4.1.5
SCHRODINGER
OPERATORS
*
232
4.1.6
SCHRODINGER
OPERATORS
THROUGH
QUADRATIC
FORMS
*
236
4.1.7
CONFINING
POTENTIALS
AND
DECAYING
POTENTIALS
*
239
4.1.8
STRONGLY
CONTINUOUS
OPERATOR
SEMIGROUPS
*
243
4.2
FEYNMAN-KAC
FORMULA
FOR
SCHRODINGER
OPERATORS
*
246
4.2.1
BOUNDED
SMOOTH
EXTERNAL
POTENTIALS
*
246
4.2.2
DERIVATION
THROUGH
THE
TROTTER
PRODUCT
FORMULA
*
249
4.2.3
KATO-CLASS
POTENTIALS
*
251
4.2.4
FEYNMAN-KAC
FORMULA
FOR
KATO-DECOMPOSABLE
POTENTIALS
*
264
4.3
PROPERTIES
OF
SCHRODINGER
OPERATORS
AND
SEMIGROUPS
-----
270
4.3.1
KERNEL
OF
THE
SCHRODINGER
SEMIGROUP
-----
270
4.3.2
POSITIVITY
IMPROVING
AND
UNIQUENESS
OF
GROUND
STATE
*
271
CONTENTS
*
VII
4.3.3
DEGENERATE
GROUND
STATE
AND
KLAUDER
PHENOMENON
*
275
4.3.4
EXISTENCE
AND
NON-EXISTENCE
OF
GROUND
STATES
*
277
4.3.5
SOJOURN
TIMES
AND
EXISTENCE
OF
BOUND
STATES
*
282
4.3.6
THE
NUMBER
OF
EIGENFUNCTIONS
WITH
NEGATIVE
EIGENVALUES
*
289
4.3.7
APPLICATION
TO
CANONICAL
COMMUTATION
RELATIONS
*
307
4.3.8
EXPONENTIAL
DECAY
OF
EIGENFUNCTIONS
*
314
4.4
FEYNMAN-KAC
FORMULA
FOR
SCHRODINGER
OPERATORS
WITH
VECTOR
POTENTIALS
-----
320
4.4.1
FEYNMAN-KAC-LTO
FORMULA
-----
320
4.4.2
ALTERNATIVE
PROOF
OF
THE
FEYNMAN-KAC-LTO
FORMULA
*
324
4.4.3
EXTENSION
TO
SINGULAR
EXTERNAL
AND
VECTOR
POTENTIALS
-----
327
4.4.4
KATO-CLASS
POTENTIALS
AND
L
P
-L
Q
BOUNDEDNESS
-----
333
4.5
FEYNMAN-KAC
FORMULA
FOR
UNBOUNDED
SEMIGROUPS
AND
STARK
EFFECT
-----
335
4.6
FEYNMAN-KAC
FORMULA
FOR
RELATIVISTIC
SCHRODINGER
OPERATORS
*
339
4.6.1
RELATIVISTIC
SCHRODINGER
OPERATOR
-----339
4.6.2
RELATIVISTIC
KATO-CLASS
POTENTIALS
*
344
4.6.3
DECAY
OF
EIGENFUNCTIONS
-----
351
4.6.4
NON-RELATIVISTIC
LIMIT
-----
356
4.7
FEYNMAN-KAC
FORMULA
FOR
SCHRODINGER
OPERATORS
WITH
SPIN
*
359
4.7.1
SCHRODINGER
OPERATORS
WITH
SPIN
J
*
359
4.7.2
A
JUMP
PROCESS
-----
361
4.7.3
FEYNMAN-KAC
FORMULA
FOR
THE
JUMP
PROCESS
*
363
4.7.4
EXTENSION
TO
SINGULAR
EXTERNAL
POTENTIALS
AND
SINGULAR
VECTOR
POTENTIALS
*
367
4.7.5
DECAY
OF
EIGENFUNCTIONS
AND
MARTINGALE
PROPERTIES
*
371
4.8
FEYNMAN-KAC
FORMULA
FOR
RELATIVISTIC
SCHRODINGER
OPERATORS
WITH
SPIN
-----
375
4.8.1
RELATIVISTIC
SCHRODINGER
OPERATOR
WITH
SPIN
|
-----
375
4.8.2
MARTINGALE
PROPERTIES
-----
381
4.8.3
DECAY
OF
EIGENFUNCTIONS
-----
384
4.9
FEYNMAN-KAC
FORMULA
FOR
NONLOCAL
SCHRODINGER
OPERATORS
-----
388
4.9.1
NONLOCAL
SCHRODINGER
OPERATORS
-----
388
4.9.2
VECTOR
POTENTIALS
----
389
4.9.3
IP-KATO-CLASS
POTENTIALS
-----
392
4.9.4
FRACTIONAL
KATO-CLASS
POTENTIALS
*
401
4.9.5
GENERALIZED
SPIN
----
406
4.9.6
RECURRENCE
PROPERTIES
AND
EXISTENCE
OF
BOUND
STATES
*
412
4.9.7
THE
NUMBER
OF
EIGENFUNCTIONS
WITH
NEGATIVE
EIGENVALUES
*
413
4.9.8
DECAY
OF
EIGENFUNCTIONS
-----
423
4.9.9
MASSLESS
RELATIVISTIC
HARMONIC
OSCILLATOR
-----432
4.9.10
EMBEDDED
EIGENVALUES
*
436
VIII
*
CONTENTS
BIBLIOGRAPHY
*
539
5
5.1
5.1.1
5.1.2
5.1.3
5.1.4
5.1.5
5.1.6
5.2
5.2.1
5.2.2
5.2.3
5.3
5.3.1
5.3.2
5.4
GIBBS
MEASURES
ASSOCIATED
WITH
FEYNMAN-KAC
SEMIGROUPS
*
449
GROUND
STATE
TRANSFORM
AND
RELATED
PROCESSES
*
449
GROUND
STATE
TRANSFORM
AND
THE
INTRINSIC
SEMIGROUP
*
449
GROUND
STATE-TRANSFORMED
PROCESSES
AS
SOLUTIONS
OF
SDE
*
454
P(0)
R
PROCESSES
WITH
CONTINUOUS
PATHS
*
458
DIRICHLET
PRINCIPLE
*
464
MEHLER
*
S
FORMULA
*
467
P(0)RPROCESSES
WITH
CADLAG
PATHS
*
476
GIBBS
MEASURES
ON
PATH
SPACE
*
481
FROM
FEYNMAN-KAC
FORMULAE
TO
GIBBS
MEASURES
*
481
GIBBS
MEASURES
ON
BROWNIAN
PATHS
*
485
GIBBS
MEASURES
ON
CADLAG
PATHS
*
492
GIBBS
MEASURES
FOR
EXTERNAL
POTENTIALS
*
494
EXISTENCE
*
494
UNIQUENESS
*
497
GIBBS
MEASURES
FOR
EXTERNAL
AND
PAIR
INTERACTION
POTENTIALS:
DIRECT
METHOD
*
503
5.5
GIBBS
MEASURES
FOR
EXTERNAL
AND
PAIR
INTERACTION
POTENTIALS:
CLUSTER
EXPANSION
*
511
5.5.1
5.5.2
5.5.3
CLUSTER
REPRESENTATION
*
511
BASIC
ESTIMATES
AND
CONVERGENCE
OF
CLUSTER
EXPANSION
*
516
FURTHER
PROPERTIES
OF
THE
GIBBS
MEASURE
*
518
6
NOTES
AND
REFERENCES
*
521
NOTES
TO
THE
PREFACE
*
521
NOTES
TO
CHAPTER
1
*
522
NOTES
TO
CHAPTER
2
*
522
NOTES
TO
CHAPTER
3
*
525
NOTES
TO
CHAPTER
4
*
526
NOTES
TO
CHAPTER
5
*
535
INDEX
*
553
|
| any_adam_object | 1 |
| author | Lőrinczi, József 1966- Hiroshima, Fumio Betz, Volker 1972- |
| author_GND | (DE-588)173059767 (DE-588)1016708270 (DE-588)123809568 |
| author_facet | Lőrinczi, József 1966- Hiroshima, Fumio Betz, Volker 1972- |
| author_role | aut aut aut |
| author_sort | Lőrinczi, József 1966- |
| author_variant | j l jl f h fh v b vb |
| building | Verbundindex |
| bvnumber | BV042905886 |
| classification_rvk | SK 620 SK 540 SK 820 SK 910 UK 4500 |
| ctrlnum | (DE-599)DNB1058497618 |
| 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 | Physik Mathematik |
| edition | 2nd edition |
| format | Book |
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| id | DE-604.BV042905886 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:12:31Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028333863 |
| open_access_boolean | |
| physical | 2 Bände |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter Studies in Mathematics |
| spelling | Lőrinczi, József 1966- Verfasser (DE-588)173059767 aut Feynman-Kac-type theorems and Gibbs measures on path space József Lőrinczi, Fumio Hiroshima, and Volker Betz 2nd edition Berlin De Gruyter [2020-2020] 2 Bände txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematics Selbstadjungierter Operator (DE-588)4180810-1 gnd rswk-swf Feynman-Kac-Formel (DE-588)4820124-8 gnd rswk-swf Gibbs-Maß (DE-588)4157328-6 gnd rswk-swf Pfadintegral (DE-588)4173973-5 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Feynman-Kac-TypeTheorems; Gibbs Measures; Quantum Field Theory; Brownian Motion Selbstadjungierter Operator (DE-588)4180810-1 s Feynman-Kac-Formel (DE-588)4820124-8 s Pfadintegral (DE-588)4173973-5 s Gibbs-Maß (DE-588)4157328-6 s Quantenfeldtheorie (DE-588)4047984-5 s Stochastische Analysis (DE-588)4132272-1 s DE-604 Hiroshima, Fumio Verfasser (DE-588)1016708270 aut Betz, Volker 1972- Verfasser (DE-588)123809568 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028333863&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lőrinczi, József 1966- Hiroshima, Fumio Betz, Volker 1972- Feynman-Kac-type theorems and Gibbs measures on path space Selbstadjungierter Operator (DE-588)4180810-1 gnd Feynman-Kac-Formel (DE-588)4820124-8 gnd Gibbs-Maß (DE-588)4157328-6 gnd Pfadintegral (DE-588)4173973-5 gnd Stochastische Analysis (DE-588)4132272-1 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4180810-1 (DE-588)4820124-8 (DE-588)4157328-6 (DE-588)4173973-5 (DE-588)4132272-1 (DE-588)4047984-5 |
| title | Feynman-Kac-type theorems and Gibbs measures on path space |
| title_auth | Feynman-Kac-type theorems and Gibbs measures on path space |
| title_exact_search | Feynman-Kac-type theorems and Gibbs measures on path space |
| title_full | Feynman-Kac-type theorems and Gibbs measures on path space József Lőrinczi, Fumio Hiroshima, and Volker Betz |
| title_fullStr | Feynman-Kac-type theorems and Gibbs measures on path space József Lőrinczi, Fumio Hiroshima, and Volker Betz |
| title_full_unstemmed | Feynman-Kac-type theorems and Gibbs measures on path space József Lőrinczi, Fumio Hiroshima, and Volker Betz |
| title_short | Feynman-Kac-type theorems and Gibbs measures on path space |
| title_sort | feynman kac type theorems and gibbs measures on path space |
| topic | Selbstadjungierter Operator (DE-588)4180810-1 gnd Feynman-Kac-Formel (DE-588)4820124-8 gnd Gibbs-Maß (DE-588)4157328-6 gnd Pfadintegral (DE-588)4173973-5 gnd Stochastische Analysis (DE-588)4132272-1 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Selbstadjungierter Operator Feynman-Kac-Formel Gibbs-Maß Pfadintegral Stochastische Analysis Quantenfeldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028333863&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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