Stochastic differential equations and applications:
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| Previous Title: | Mao, Xuerong Stochastic differential equations and their applications |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
Chichester
Horwood Publ.
2008
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 411-418) and index |
| Physical Description: | XVIII, 422 S. |
| ISBN: | 9781904275343 1904275346 |
Staff View
MARC
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| 100 | 1 | |a Mao, Xuerong |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stochastic differential equations and applications |c Xuerong Mao |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Chichester |b Horwood Publ. |c 2008 | |
| 300 | |a XVIII, 422 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references (p. 411-418) and index | ||
| 650 | 4 | |a Stochastic differential equations | |
| 650 | 0 | 7 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |2 gnd |9 rswk-swf |
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| 780 | 0 | 0 | |i 1. Auflage |a Mao, Xuerong |t Stochastic differential equations and their applications |
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Record in the Search Index
| _version_ | 1804138065737809920 |
|---|---|
| adam_text | Contents
Preface
to the Second Edition
vii
Preface to the First Edition
ix
General Notation
xv
1.
Brownian Motions and Stochastic Integrals
1
1.1.
Introduction
1
1.2.
Basic notations of probability theory
2
1.3.
Stochastic processes
9
1.4.
Brownian motions
15
1.5.
Stochastic integrals
18
1.6.
Itô s
formula
31
1.7.
Moment inequalities
39
1.8.
Gronwall-type inequalities
44
2.
Stochastic Differential Equations
47
2.1.
Introduction
47
2.2.
Stochastic differential equations
48
2.3.
Existence and uniqueness of solutions
51
2.4.
LP-estimates
59
2.5.
Almost surely asymptotic estimates
63
2.6.
Caratheodory s approximate solutions
71
2.7.
Euler-Maruyama s approximate solutions
76
2.8.
SDE and PDE: Feynman-Kac s formula
78
2.9.
Solutions as Markov processes
84
3.
Linear Stochastic Differential
Equations
91
3.1.
Introduction
91
3.2.
Stochastic Liouville s formula
92
3.3.
The variation-of-constants formula
96
3.4.
Case studies
98
3.5.
Examples
101
4.
Stability of Stochastic Differential Equations
107
4.1.
Introduction
107
xi
xii
Contents
4.2.
Stability in probability
110
4.3.
Almost sure exponential stability
119
4.4.
Moment exponential stability
127
4.5.
Stochastic stabilization and destabilization
135
4.6.
Further topics
141
5.
Stochastic Functional Differential Equations
147
5.1.
Introduction
147
5.2.
Existence-and-uniqueness theorems
149
5.3.
Stochastic differential delay equations
156
5.4.
Exponential estimates
160
5.5.
Approximate solutions
164
5.6.
Stability theory
—
Razumikhin theorems
171
5.7.
Stochastic self-stabilization
190
6.
Stochastic Equations of Neutral Type
201
6.1.
Introduction
201
6.2.
Neutral stochastic functional differential equations
203
6.3.
Neutral stochastic differential delay solutions
209
6.4.
Moment and pathwise estimates
211
6.5.
jy-continuity
217
6.6.
Exponential stability
221
7.
Backward Stochastic Differential Equations
235
7.1.
Introduction
235
7.2.
Martingale representation theorem
236
7.3.
Equations with Lipschitz coefficients
241
7.4.
Equations with non-Lipschitz coefficients
248
7.5.
Regularities
260
7.6.
BSDE and
quasilinear PDE 267
8.
Stochastic Oscillators
271
8.1.
Introduction
271
8.2.
The Cameron-Martin-Girsanov theorem
272
8.3.
Nonlinear stochastic oscillators
274
8.4.
Linear stochastic oscillators
278
8.5.
Energy bounds
288
9.
Applications to Economics and Finance
301
9.1.
Introduction 301
9.2.
Stochastic modelling in asset prices
301
9.3.
Options and their values
314
9.4.
Optimal stopping problems
329
9.5.
Stochastic games
343
10.
Stochastic Neural Networks 351
10.1.
Introduction
351
10.2.
Stochastic neural networks
351
10.3.
Stochastic neural networks with delays
366
Contents xiii
11.
Stochastic Delay Population Systems
377
11.1.
Introduction
377
11.2.
Noise independent of population sizes
381
11.3.
Noise dependent on population sizes: Part I
390
11.4.
Noise dependent on population sizes: Part II
396
11.5.
Stochastic delay
Lotka-
Volterra food chain
406
Bibliographical Notes
409
References
411
Index
419
|
| adam_txt |
Contents
Preface
to the Second Edition
vii
Preface to the First Edition
ix
General Notation
xv
1.
Brownian Motions and Stochastic Integrals
1
1.1.
Introduction
1
1.2.
Basic notations of probability theory
2
1.3.
Stochastic processes
9
1.4.
Brownian motions
15
1.5.
Stochastic integrals
18
1.6.
Itô's
formula
31
1.7.
Moment inequalities
39
1.8.
Gronwall-type inequalities
44
2.
Stochastic Differential Equations
47
2.1.
Introduction
47
2.2.
Stochastic differential equations
48
2.3.
Existence and uniqueness of solutions
51
2.4.
LP-estimates
59
2.5.
Almost surely asymptotic estimates
63
2.6.
Caratheodory's approximate solutions
71
2.7.
Euler-Maruyama's approximate solutions
76
2.8.
SDE and PDE: Feynman-Kac's formula
78
2.9.
Solutions as Markov processes
84
3.
Linear Stochastic Differential
Equations
91
3.1.
Introduction
91
3.2.
Stochastic Liouville's formula
92
3.3.
The variation-of-constants formula
96
3.4.
Case studies
98
3.5.
Examples
101
4.
Stability of Stochastic Differential Equations
107
4.1.
Introduction
107
xi
xii
Contents
4.2.
Stability in probability
110
4.3.
Almost sure exponential stability
119
4.4.
Moment exponential stability
127
4.5.
Stochastic stabilization and destabilization
135
4.6.
Further topics
141
5.
Stochastic Functional Differential Equations
147
5.1.
Introduction
147
5.2.
Existence-and-uniqueness theorems
149
5.3.
Stochastic differential delay equations
156
5.4.
Exponential estimates
160
5.5.
Approximate solutions
164
5.6.
Stability theory
—
Razumikhin theorems
171
5.7.
Stochastic self-stabilization
190
6.
Stochastic Equations of Neutral Type
201
6.1.
Introduction
201
6.2.
Neutral stochastic functional differential equations
203
6.3.
Neutral stochastic differential delay solutions
209
6.4.
Moment and pathwise estimates
211
6.5.
jy-continuity
217
6.6.
Exponential stability
221
7.
Backward Stochastic Differential Equations
235
7.1.
Introduction
235
7.2.
Martingale representation theorem
236
7.3.
Equations with Lipschitz coefficients
241
7.4.
Equations with non-Lipschitz coefficients
248
7.5.
Regularities
260
7.6.
BSDE and
quasilinear PDE 267
8.
Stochastic Oscillators
271
8.1.
Introduction
271
8.2.
The Cameron-Martin-Girsanov theorem
272
8.3.
Nonlinear stochastic oscillators
274
8.4.
Linear stochastic oscillators
278
8.5.
Energy bounds
288
9.
Applications to Economics and Finance
301
9.1.
Introduction 301
9.2.
Stochastic modelling in asset prices
301
9.3.
Options and their values
314
9.4.
Optimal stopping problems
329
9.5.
Stochastic games
343
10.
Stochastic Neural Networks 351
10.1.
Introduction
351
10.2.
Stochastic neural networks
351
10.3.
Stochastic neural networks with delays
366
Contents xiii
11.
Stochastic Delay Population Systems
377
11.1.
Introduction
377
11.2.
Noise independent of population sizes
381
11.3.
Noise dependent on population sizes: Part I
390
11.4.
Noise dependent on population sizes: Part II
396
11.5.
Stochastic delay
Lotka-
Volterra food chain
406
Bibliographical Notes
409
References
411
Index
419 |
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| id | DE-604.BV035102729 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:14:46Z |
| indexdate | 2024-07-09T21:22:16Z |
| institution | BVB |
| isbn | 9781904275343 1904275346 |
| language | English |
| lccn | 2008411866 |
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| physical | XVIII, 422 S. |
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| spelling | Mao, Xuerong Verfasser aut Stochastic differential equations and applications Xuerong Mao 2. ed. Chichester Horwood Publ. 2008 XVIII, 422 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 411-418) and index Stochastic differential equations Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 1. Auflage Mao, Xuerong Stochastic differential equations and their applications Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016770685&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mao, Xuerong Stochastic differential equations and applications Stochastic differential equations Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4057621-8 |
| title | Stochastic differential equations and applications |
| title_auth | Stochastic differential equations and applications |
| title_exact_search | Stochastic differential equations and applications |
| title_exact_search_txtP | Stochastic differential equations and applications |
| title_full | Stochastic differential equations and applications Xuerong Mao |
| title_fullStr | Stochastic differential equations and applications Xuerong Mao |
| title_full_unstemmed | Stochastic differential equations and applications Xuerong Mao |
| title_old | Mao, Xuerong Stochastic differential equations and their applications |
| title_short | Stochastic differential equations and applications |
| title_sort | stochastic differential equations and applications |
| topic | Stochastic differential equations Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Stochastic differential equations Stochastische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016770685&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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