Fluctuation theory for Lévy processes: École d'Été de Probabilités de Saint-Flour XXXV - 2005
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| Main Author: | |
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| Other Authors: | |
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2007
|
| Series: | Lecture notes in mathematics
1897 : École d'Été de Probabilités de Saint-Flour |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 147 S. |
| ISBN: | 9783540485100 3540485104 |
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| 245 | 1 | 0 | |a Fluctuation theory for Lévy processes |b École d'Été de Probabilités de Saint-Flour XXXV - 2005 |c Ronald A. Doney. Ed.: Jean Picard |
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Record in the Search Index
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| adam_text | Contents
Introduction
to Levy Processes
............................ 1
1.1
Notation
............................................... 1
1.2
Poisson
Point Processes
.................................. 3
1.3
The
Lévy-Itô
Decomposition
.............................. 5
1.4
Levy Processes as Markov Processes
....................... 7
Subordinators
............................................. 9
2.1
Introduction
............................................ 9
2.2
Basics
.................................................. 9
2.3
The Renewal Measure
.................................... 10
2.4
Passage Across a Level
................................... 13
2.5
Arc-Sine Laws for Subordinators
.......................... 15
2.6
Rates of Growth
........................................ 16
2.7
Killed Subordinators
..................................... 17
Local Times and Excursions
............................... 19
3.1
Introduction
............................................ 19
3.2
Local Time of a Markov Process
........................... 19
3.3
The Regular, Instantaneous Case
.......................... 20
3.4
The Excursion Process
................................... 22
3.5
The Case of Holding and Irregular Points
................... 23
Ladder Processes and the Wiener—
Hopf
Factorisation
...... 25
4.1
Introduction
............................................ 25
4.2
The Random Walk Case
.................................. 25
4.3
The Reflected and Ladder Processes
....................... 27
4.4
Applications
............................................ 30
4.5
A Stochastic Bound
...................................... 35
VIII Contents
5 Further Wiener-Hopf
Developments
....................... 41
5.1
Introduction
............................................ 41
5.2
Extensions of a Result due to Baxter
....................... 41
5.3
Les
Equations
Amicales
of Vigon
.......................... 43
5.4
A First Passage Quintuple Identity
........................ 49
6
Creeping and Related Questions
........................... 51
6.1
Introduction
............................................ 51
6.2
Notation and Preliminary Results
......................... 52
6.3
The Mean Ladder Height Problem
......................... 53
6.4
Creeping
............................................... 56
6.5
Limit Points of the Supremum Process
..................... 59
6.6
Regularity of the Half-Line
............................... 61
6.7
Summary: Four Integral Tests
............................. 64
7
Spitzer s Condition
........................................ 65
7.1
Introduction
............................................ 65
7.2
Proofs
................................................. 65
7.2.1
The Case
ρ
= 0,1 ................................. 66
7.2.2
A First Proof for the Case
0 <
ρ
< 1................. 66
7.2.3
A Second Proof for the Case
0 <
ρ
< 1............... 68
7.3
Further Results
......................................... 69
7.4
Tailpiece
............................................... 80
8
Levy Processes Conditioned to Stay Positive
.............. 81
8.1
Introduction
............................................ 81
8.2
Notation and Preliminaries
............................... 81
8.3
Definition and Path Decomposition
........................ 83
8.4
The Convergence Result
.................................. 86
8.5
Pathwise Constructions of (X,PT)
......................... 89
8.5.1
Tanaka s Construction
............................. 89
8.5.2
Bertoin s Construction
............................. 91
9
Spectrally Negative Levy Processes
........................ 95
9.1
Introduction
............................................ 95
9.2
Basics
.................................................. 95
9.3
The Random Walk Case
.................................
9.4
The Scale Function
...................................... 100
9.5
Further Developments
....................................
I04
9.6
Exit Problems for the Reflected Process
..............
109
9.7
Addendum
........ ....... 112
Contents
IX
10
Small-Time Behaviour
.....................................115
10.1
Introduction
............................................115
10.2
Notation and Preliminary Results
.........................115
10.3
Convergence in Probability
...............................117
10.4
Almost Sure Results
.....................................126
10.5
Summary of Asymptotic Results
..........................131
10.5.1
Laws of Large Numbers
............................131
10.5.2
Central Limit Theorems
............................131
10.5.3
Exit from a Symmetric Interval
.....................132
References
.....................................................133
Index
..........................................................139
List of Participants
............................................141
List of Short Lectures
.........................................145
|
| adam_txt |
Contents
Introduction
to Levy Processes
. 1
1.1
Notation
. 1
1.2
Poisson
Point Processes
. 3
1.3
The
Lévy-Itô
Decomposition
. 5
1.4
Levy Processes as Markov Processes
. 7
Subordinators
. 9
2.1
Introduction
. 9
2.2
Basics
. 9
2.3
The Renewal Measure
. 10
2.4
Passage Across a Level
. 13
2.5
Arc-Sine Laws for Subordinators
. 15
2.6
Rates of Growth
. 16
2.7
Killed Subordinators
. 17
Local Times and Excursions
. 19
3.1
Introduction
. 19
3.2
Local Time of a Markov Process
. 19
3.3
The Regular, Instantaneous Case
. 20
3.4
The Excursion Process
. 22
3.5
The Case of Holding and Irregular Points
. 23
Ladder Processes and the Wiener—
Hopf
Factorisation
. 25
4.1
Introduction
. 25
4.2
The Random Walk Case
. 25
4.3
The Reflected and Ladder Processes
. 27
4.4
Applications
. 30
4.5
A Stochastic Bound
. 35
VIII Contents
5 Further Wiener-Hopf
Developments
. 41
5.1
Introduction
. 41
5.2
Extensions of a Result due to Baxter
. 41
5.3
Les
Equations
Amicales
of Vigon
. 43
5.4
A First Passage Quintuple Identity
. 49
6
Creeping and Related Questions
. 51
6.1
Introduction
. 51
6.2
Notation and Preliminary Results
. 52
6.3
The Mean Ladder Height Problem
. 53
6.4
Creeping
. 56
6.5
Limit Points of the Supremum Process
. 59
6.6
Regularity of the Half-Line
. 61
6.7
Summary: Four Integral Tests
. 64
7
Spitzer's Condition
. 65
7.1
Introduction
. 65
7.2
Proofs
. 65
7.2.1
The Case
ρ
= 0,1 . 66
7.2.2
A First Proof for the Case
0 <
ρ
< 1. 66
7.2.3
A Second Proof for the Case
0 <
ρ
< 1. 68
7.3
Further Results
. 69
7.4
Tailpiece
. 80
8
Levy Processes Conditioned to Stay Positive
. 81
8.1
Introduction
. 81
8.2
Notation and Preliminaries
. 81
8.3
Definition and Path Decomposition
. 83
8.4
The Convergence Result
. 86
8.5
Pathwise Constructions of (X,PT)
. 89
8.5.1
Tanaka's Construction
. 89
8.5.2
Bertoin's Construction
. 91
9
Spectrally Negative Levy Processes
. 95
9.1
Introduction
. 95
9.2
Basics
. 95
9.3
The Random Walk Case
. "
9.4
The Scale Function
. 100
9.5
Further Developments
.
I04
9.6
Exit Problems for the Reflected Process
.
109
9.7
Addendum
. . 112
Contents
IX
10
Small-Time Behaviour
.115
10.1
Introduction
.115
10.2
Notation and Preliminary Results
.115
10.3
Convergence in Probability
.117
10.4
Almost Sure Results
.126
10.5
Summary of Asymptotic Results
.131
10.5.1
Laws of Large Numbers
.131
10.5.2
Central Limit Theorems
.131
10.5.3
Exit from a Symmetric Interval
.132
References
.133
Index
.139
List of Participants
.141
List of Short Lectures
.145 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:25:19Z |
| indexdate | 2024-07-09T20:57:12Z |
| institution | BVB |
| isbn | 9783540485100 3540485104 |
| language | English |
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| physical | IX, 147 S. |
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| series2 | Lecture notes in mathematics |
| spelling | Doney, Ronald A. Verfasser aut Fluctuation theory for Lévy processes École d'Été de Probabilités de Saint-Flour XXXV - 2005 Ronald A. Doney. Ed.: Jean Picard Berlin [u.a.] Springer 2007 IX, 147 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1897 : École d'Été de Probabilités de Saint-Flour Lévy-Prozess Lévy processes Lévy-Prozess (DE-588)4463623-4 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Lévy-Prozess (DE-588)4463623-4 s DE-604 Picard, Jean edt Lecture notes in mathematics 1897 : École d'Été de Probabilités de Saint-Flour (DE-604)BV000676446 1897 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015628191&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Doney, Ronald A. Fluctuation theory for Lévy processes École d'Été de Probabilités de Saint-Flour XXXV - 2005 Lecture notes in mathematics Lévy-Prozess Lévy processes Lévy-Prozess (DE-588)4463623-4 gnd |
| subject_GND | (DE-588)4463623-4 (DE-588)1071861417 |
| title | Fluctuation theory for Lévy processes École d'Été de Probabilités de Saint-Flour XXXV - 2005 |
| title_auth | Fluctuation theory for Lévy processes École d'Été de Probabilités de Saint-Flour XXXV - 2005 |
| title_exact_search | Fluctuation theory for Lévy processes École d'Été de Probabilités de Saint-Flour XXXV - 2005 |
| title_exact_search_txtP | Fluctuation theory for Lévy processes École d'Été de Probabilités de Saint-Flour XXXV - 2005 |
| title_full | Fluctuation theory for Lévy processes École d'Été de Probabilités de Saint-Flour XXXV - 2005 Ronald A. Doney. Ed.: Jean Picard |
| title_fullStr | Fluctuation theory for Lévy processes École d'Été de Probabilités de Saint-Flour XXXV - 2005 Ronald A. Doney. Ed.: Jean Picard |
| title_full_unstemmed | Fluctuation theory for Lévy processes École d'Été de Probabilités de Saint-Flour XXXV - 2005 Ronald A. Doney. Ed.: Jean Picard |
| title_short | Fluctuation theory for Lévy processes |
| title_sort | fluctuation theory for levy processes ecole d ete de probabilites de saint flour xxxv 2005 |
| title_sub | École d'Été de Probabilités de Saint-Flour XXXV - 2005 |
| topic | Lévy-Prozess Lévy processes Lévy-Prozess (DE-588)4463623-4 gnd |
| topic_facet | Lévy-Prozess Lévy processes Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015628191&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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