Approximation and weak convergence methods for random processes, with applications to stochastic systems theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, Mass. u.a.
MIT Pr.
1984
|
| Series: | The MIT Press series in signal processing, optimization and control
6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 269 S. |
| ISBN: | 0262110903 |
Staff View
MARC
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| 245 | 1 | 0 | |a Approximation and weak convergence methods for random processes, with applications to stochastic systems theory |
| 264 | 1 | |a Cambridge, Mass. u.a. |b MIT Pr. |c 1984 | |
| 300 | |a XVII, 269 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a The MIT Press series in signal processing, optimization and control |v 6 | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Convergence | |
| 650 | 4 | |a Stochastic processes | |
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Record in the Search Index
| _version_ | 1804114818849832960 |
|---|---|
| adam_text | Contents
Series
Foreword
xi
Introduction
xiii
1
Review of Stochastic Processes
1
1
Martingales
3
2
The Wiener Process and Stochastic Integrals
5
3
Itô s
Lemma
9
4
Stochastic Differential Equations
11
5
The Martingale Problem
15
6
Jump Diffusion Processes
20
2
Weak Convergence
23
1
Introduction
23
2
Definitions and Motivation
25
3
General Weak Convergence Theorems
28
4
The Spaces
Cr[0,
Τ]
and £>r[0,
Τ], Τ
<
oo
30
3
Weak Convergence Methods
34
1
Introduction
34
2
The Perturbed Test Function Method
36
3
Tightness
47
4
The Discrete Parameter Case
51
5
Convergence of Finite-Dimensional Distributions and the
Kato-Trotter Theorem
52
4
The Perturbed Test Function Method
56
1
Introduction
56
2
ODE Limits: State-Independent Noise
57
3
The Discrete Parameter Case: State-Independent Noise and ODE
Limits
67
4
State-Dependent Noise and Nonsmooth Dynamics: Discrete
Parameter
69
5
The Continuous Parameter Case: State-Dependent Noise
74
6
Diffusion Limits: Smooth Dynamics and Continuous
Parameter
78
viii Contents
7 Diffusion Limits:
Discrete
Parameter 87
8
A
Special
case: A User s Guide
91
9
The Discrete Parameter Case: State-Dependent Noise, Diffusion
Limits
93
S
Weak Convergence by a Direct-Averaging Method
97
1
Introduction
97
2
Noise Independent of the State: ODE Limit
99
3
Discrete Parameter Case: ODE Limit and State-Dependent
Noise
105
4
A Projection Algorithm
114
5
Continuous Parameter Case: ODE Limit and State-Dependent
Noise
116
6
Diffusion Limit
121
7
Jump Process Limit
123
8
The Direct-
A
veraging
Method with Perturbed Test Functions
126
9
A Stochastic Approximation Example
138
6
Stability and Asymptotic and Invariant Measures
141
1
Introduction
141
2
Tightness and Stability for
Ito
Processes
144
3
Recurrence, Path Excursion Estimates, and Moment Boundedness
for^()
148
4
Asymptotic Measures of the {xe(t)}
153
5
Convergence When
(х°(
■ ),
ξε(
■ ))
Is Markov
156
6
A Sufficient Condition for Tightness; Constructing a Perturbed
Liapunov Function
158
7
Nonsmooth Dynamics and/or State-Dependent Noise
163
8
Unbounded Noise
166
9
The Discrete Parameter Case
171
10
Stability w.p.
1,
and Weak Convergence for Stochastic
Approximations
173
7
Singular Perturbations
175
1
Introduction
175
Contents ix
2
The Direct-Averaging Method
175
3
On the Stability and Tightness Assumptions
181
4
The Direct-Averaging Method with Perturbed Test Functions
187
8
Applications I
189
1
Adaptive Antenna Arrays: Weak Convergence of the Array
Weights
189
2
Adaptive Antenna Arrays: Asymptotic Properties for Large Time
and Normalized Errors
193
3
An Adaptive Equalizer
199
4
An Adaptive Quantizer
204
5
Rate of Convergence for Stochastic Approximations
206
9
Applications II
211
1
The Wong-Zakai Problem
211
2
A Runge-Kutta Method for Solving a Stochastic Differential
Equation
214
3
The Output Process of a Hard
Limiter
215
10
Applications III: Synchronization Systems
223
1
A Standard Phase-Locked Loop
224
2
A Phase-Locked Loop with
a Limiter
231
11
The Theory of Large Deviations and Applications
239
1
Introduction
239
2
Basic Results: The Systems and Action Functionals
241
3
The Idea of Large Deviations and Chernoff Bounds
245
4
The Freidlin-Gartner Approach to Large Deviations
Estimates
249
5
Escape Time Estimates
254
6
Applications and Examples
256
References
261
Index
267
|
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| dewey-raw | 519.2 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000351851 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:12:46Z |
| institution | BVB |
| isbn | 0262110903 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000218743 |
| oclc_num | 9622486 |
| open_access_boolean | |
| owner | DE-12 DE-739 DE-706 DE-473 DE-BY-UBG |
| owner_facet | DE-12 DE-739 DE-706 DE-473 DE-BY-UBG |
| physical | XVII, 269 S. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | MIT Pr. |
| record_format | marc |
| series | The MIT Press series in signal processing, optimization and control |
| series2 | The MIT Press series in signal processing, optimization and control |
| spelling | Kushner, Harold J. 1933- Verfasser (DE-588)11559163X aut Approximation and weak convergence methods for random processes, with applications to stochastic systems theory Cambridge, Mass. u.a. MIT Pr. 1984 XVII, 269 S. txt rdacontent n rdamedia nc rdacarrier The MIT Press series in signal processing, optimization and control 6 Approximation theory Convergence Stochastic processes Stochastic systems Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Schwache Konvergenz (DE-588)4180292-5 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Schwache Konvergenz (DE-588)4180292-5 s DE-604 Approximation (DE-588)4002498-2 s The MIT Press series in signal processing, optimization and control 6 (DE-604)BV000011426 6 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000218743&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kushner, Harold J. 1933- Approximation and weak convergence methods for random processes, with applications to stochastic systems theory The MIT Press series in signal processing, optimization and control Approximation theory Convergence Stochastic processes Stochastic systems Stochastischer Prozess (DE-588)4057630-9 gnd Schwache Konvergenz (DE-588)4180292-5 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4180292-5 (DE-588)4002498-2 |
| title | Approximation and weak convergence methods for random processes, with applications to stochastic systems theory |
| title_auth | Approximation and weak convergence methods for random processes, with applications to stochastic systems theory |
| title_exact_search | Approximation and weak convergence methods for random processes, with applications to stochastic systems theory |
| title_full | Approximation and weak convergence methods for random processes, with applications to stochastic systems theory |
| title_fullStr | Approximation and weak convergence methods for random processes, with applications to stochastic systems theory |
| title_full_unstemmed | Approximation and weak convergence methods for random processes, with applications to stochastic systems theory |
| title_short | Approximation and weak convergence methods for random processes, with applications to stochastic systems theory |
| title_sort | approximation and weak convergence methods for random processes with applications to stochastic systems theory |
| topic | Approximation theory Convergence Stochastic processes Stochastic systems Stochastischer Prozess (DE-588)4057630-9 gnd Schwache Konvergenz (DE-588)4180292-5 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | Approximation theory Convergence Stochastic processes Stochastic systems Stochastischer Prozess Schwache Konvergenz Approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000218743&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000011426 |
| work_keys_str_mv | AT kushnerharoldj approximationandweakconvergencemethodsforrandomprocesseswithapplicationstostochasticsystemstheory |