Stochastic stability and control:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Acad. Press
1967
|
| Series: | Mathematics in science and engineering
33 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 161 S. graph. Darst. |
Staff View
MARC
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| 100 | 1 | |a Kushner, Harold J. |d 1933- |e Verfasser |0 (DE-588)11559163X |4 aut | |
| 245 | 1 | 0 | |a Stochastic stability and control |c Harold J. Kushner |
| 264 | 1 | |a New York [u.a.] |b Acad. Press |c 1967 | |
| 300 | |a XIV, 161 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics in science and engineering |v 33 | |
| 650 | 4 | |a Liapounov, Fonctions de | |
| 650 | 4 | |a Processus de Markov | |
| 650 | 4 | |a Théorie de la commande | |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Kontrolltheorie |0 (DE-588)4032317-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stabilität |0 (DE-588)4056693-6 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804117214726455296 |
|---|---|
| adam_text | Contents
Preface
.................... ix
I
/
Introduction
................ 1
1.
Markov Processes
............... 1
Discrete time Markov process
1,
Continuous time Markov processes
3,
Notation
4,
Continuity
4
2.
Strong Markov Processes
............. 4
Markov time
5,
Strong Markov process
5,
Discrete parameter pro¬
cesses
7,
Feller processes
8,
Weak infinitesimal operator of a strong
Markov process
9,
Dynkin s formula
10
3.
Stopped Processes
...............11
4.
Ito
Processes
......-..........12
Strong Markov property
15,
Differential generator
15,
Itô s
lemma
16,
Stopped processes
17,
Weakening of condition
(4-5) 18
5.
Poisson
Differential Equations
...........18
Second form of the
Poisson
equation
20
6.
Strong Diffusion Processes
............22
7.
Martingales
................25
II
/
Stochastic Stability
.............27
1.
Introduction
................27
Definitions
30,
The idea of a Liapunov function
33,
The stochastic
Liapunov function approach
34,
History
35
2.
Theorems. Continuous Parameter
..........36
Assumptions
36,
Definition
39,
Remark on time dependence
41,
Remark on strong diffusion processes
44
3.
Examples
.................55
4.
Discrete Parameter Stability
............71
5.
On the Construction of Stochastic Liapunov Functions
.... 72
ХІІІ
XIV CONTENTS
III
/
Finite Time Stability and First Exit Times
.....77
1.
Introduction
................77
2.
Theorems
.................79
Strong diffusion processes
89
3.
Examples
.................91
Improving the bound
100
IV
/
Optimal Stochastic Control
..........102
1.
Introduction
................102
A dynamic programming algorithm
103,
Discussion
106,
A deter¬
ministic result
107,
The stochastic analog
108
2.
Theorems
.................109
Terminology
109,
A particular form for F(V(x))
118,
An optimality
theorem
118,
Control over a fixed time interval
121,
Strong diffusion
process
124,
General
nonanticipati ve
comparison controls
126,
Practical optimality : Compactifying the state space
128
3.
Examples
.................130
4.
A Discrete Parameter Theorem
...........141
V
/
The Design of Controls
............143
1.
Introduction
................143
2.
The Calculation of Controls Which Assure a Given Stability
Property
.................144
3.
Design of Controls to Decrease the Cost
........147
The Liapunov function approach to design
150
References
...................153
Author Index
..................159
Subject Index
..................160
|
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| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:50:51Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001828641 |
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| physical | XIV, 161 S. graph. Darst. |
| publishDate | 1967 |
| publishDateSearch | 1967 |
| publishDateSort | 1967 |
| publisher | Acad. Press |
| record_format | marc |
| series | Mathematics in science and engineering |
| series2 | Mathematics in science and engineering |
| spelling | Kushner, Harold J. 1933- Verfasser (DE-588)11559163X aut Stochastic stability and control Harold J. Kushner New York [u.a.] Acad. Press 1967 XIV, 161 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics in science and engineering 33 Liapounov, Fonctions de Processus de Markov Théorie de la commande Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastische Kontrolltheorie (DE-588)4263657-7 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Stochastische Kontrolltheorie (DE-588)4263657-7 s DE-604 Stochastischer Prozess (DE-588)4057630-9 s Stabilität (DE-588)4056693-6 s Kontrolltheorie (DE-588)4032317-1 s 1\p DE-604 Mathematics in science and engineering 33 (DE-604)BV000001196 33 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001828641&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kushner, Harold J. 1933- Stochastic stability and control Mathematics in science and engineering Liapounov, Fonctions de Processus de Markov Théorie de la commande Stochastischer Prozess (DE-588)4057630-9 gnd Stochastische Kontrolltheorie (DE-588)4263657-7 gnd Kontrolltheorie (DE-588)4032317-1 gnd Stabilität (DE-588)4056693-6 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4263657-7 (DE-588)4032317-1 (DE-588)4056693-6 |
| title | Stochastic stability and control |
| title_auth | Stochastic stability and control |
| title_exact_search | Stochastic stability and control |
| title_full | Stochastic stability and control Harold J. Kushner |
| title_fullStr | Stochastic stability and control Harold J. Kushner |
| title_full_unstemmed | Stochastic stability and control Harold J. Kushner |
| title_short | Stochastic stability and control |
| title_sort | stochastic stability and control |
| topic | Liapounov, Fonctions de Processus de Markov Théorie de la commande Stochastischer Prozess (DE-588)4057630-9 gnd Stochastische Kontrolltheorie (DE-588)4263657-7 gnd Kontrolltheorie (DE-588)4032317-1 gnd Stabilität (DE-588)4056693-6 gnd |
| topic_facet | Liapounov, Fonctions de Processus de Markov Théorie de la commande Stochastischer Prozess Stochastische Kontrolltheorie Kontrolltheorie Stabilität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001828641&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001196 |
| work_keys_str_mv | AT kushnerharoldj stochasticstabilityandcontrol |