Numerical methods for stochastic control problems in continuous time:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
[2001]
|
| Edition: | second edition |
| Series: | Applications of mathematics
24 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 475 Seiten Diagramme |
| ISBN: | 0387951393 9780387951393 9781461300076 |
Staff View
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| 245 | 1 | 0 | |a Numerical methods for stochastic control problems in continuous time |c Harold J. Kushner ; Paul Dupuis |
| 250 | |a second edition | ||
| 264 | 1 | |a New York |b Springer |c [2001] | |
| 264 | 4 | |c © 2001 | |
| 300 | |a xii, 475 Seiten |b Diagramme | ||
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| 490 | 1 | |a Applications of mathematics |v 24 | |
| 650 | 4 | |a Bibliographie enthalten / Bibliography included - 3 | |
| 650 | 4 | |a Lehrbuch / Textbook - 28 | |
| 650 | 4 | |a Numerisches Verfahren / Stochastischer Prozess / Markovscher Prozess / Theorie | |
| 650 | 4 | |a Stochastic control theory | |
| 650 | 4 | |a Markov processes | |
| 650 | 4 | |a Numerical analysis | |
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Record in the Search Index
| _version_ | 1804128818126913536 |
|---|---|
| adam_text | HAROLD J. KUSHNER PAUL DUPUIS NUMERICAL METHODS FOR STOCHASTIC CONTROL
PROBLEMS IN CONTINUOUS TIME SECOND EDITION WITH 40 FIGURES SPRINGER
CONTENTS INTRODUCTION 1 REVIEW OF CONTINUOUS TIME MODELS 7 1.1
MARTINGALES AND MARTINGALE INEQUALITIES 8 1.2 STOCHASTIC INTEGRATION 9
1.3 STOCHASTIC DIFFERENTIAL EQUATIONS: DIFFUSIONS 14 1.4 REFLECTED
DIFFUSIONS 21 1.5 PROCESSES WITH JUMPS 28 CONTROLLED MARKOV CHAINS 35
2.1 RECURSIVE EQUATIONS FOR THE COST 36 2.1.1 STOPPING ON FIRST EXIT
FROM A GIVEN SET 36 2.1.2 DISCOUNTED COST 38 2.1.3 AVERAGE COST PER UNIT
TIME 40 2.1.4 STOPPING AT A GIVEN TERMINAL TIME 41 2.2 OPTIMAL STOPPING
PROBLEMS 42 2.2.1 DISCOUNTED COST 43 2.2.2 UNDISCOUNTED COST 47 2.3
DISCOUNTED COST 48 2.4 CONTROL TO A TARGET SET AND CONTRACTION MAPPINGS
50 2.5 FINITE TIME CONTROL PROBLEMS 52 DYNAMIC PROGRAMMING EQUATIONS 53
3.1 FUNCTIONALS OF UNCONTROLLED PROCESSES 54 VIII CONTENTS 3.1.1 COST
UNTIL A TARGET SET IS REACHED 54 3.1.2 THE DISCOUNTED COST 56 3.1.3 A
REFLECTING BOUNDARY 57 3.1.4 THE AVERAGE COST PER UNIT TIME 58 3.1.5 THE
COST OVER A FIXED FINITE TIME INTERVAL 59 3.1.6 A JUMP DIFFUSION EXAMPLE
59 3.2 THE OPTIMAL STOPPING PROBLEM 60 3.3 CONTROL UNTIL A TARGET SET IS
REACHED 61 3.4 A DISCOUNTED PROBLEM WITH A TARGET SET AND REFLECTION . .
65 3.5 AVERAGE COST PER UNIT TIME 65 4 MARKOV CHAIN APPROXIMATION
METHOD: INTRODUCTION 67 4.1 MARKOV CHAIN APPROXIMATION 69 4.2 CONTINUOUS
TIME INTERPOLATION 72 4.3 A MARKOV CHAIN INTERPOLATION 74 4.4 A RANDOM
WALK APPROXIMATION 78 4.5 A DETERMINISTIC DISCOUNTED PROBLEM 80 4.6
DETERMINISTIC RELAXED CONTROLS 85 5 CONSTRUCTION OF THE APPROXIMATING
MARKOV CHAINS 89 5.1 ONE DIMENSIONAL EXAMPLES 91 5.2 NUMERICAL
SIMPLIFICATIONS 99 5.2.1 ELIMINATING THE CONTROL DEPENDENCE IN THE
DENOMINATORS OF P H {X,Y A) AND AT H (X, A) 99 5.2.2 A USEFUL
NORMALIZATION IF P H (X,X A) ^ 0 100 5.2.3 ALTERNATIVE MARKOV CHAIN
APPROXIMATIONS FOR EXAMPLE 4 OF SECTION 5.1: SPLITTING THE OPERATOR . .
103 5.3 THE GENERAL FINITE DIFFERENCE METHOD 106 5.3.1 THE GENERAL CASE
108 5.3.2 A TWO DIMENSIONAL EXAMPLE: SPLITTING THE OPERATORS 112 5.4 A
DIRECT CONSTRUCTION 113 5.4.1 AN INTRODUCTORY EXAMPLE 114 5.4.2 EXAMPLE
2. A DEGENERATE COVARIANCE MATRIX 117 5.4.3 EXAMPLE 3 119 5.4.4 A
GENERAL METHOD 121 5.5 VARIABLE GRIDS 122 5.6 JUMP DIFFUSION PROCESSES
127 5.6.1 THE JUMP DIFFUSION PROCESS MODEL: RECAPITULATION . 127 5.6.2
CONSTRUCTING THE APPROXIMATING MARKOV CHAIN . . . 128 5.6.3 A CONVENIENT
REPRESENTATION OF {, N OO} AND V H (-) 131 5.7 REFLECTING BOUNDARIES
132 5.7.1 GENERAL DISCUSSION 132 5.7.2 LOCALLY CONSISTENT APPROXIMATIONS
ON THE BOUNDARY . 136 CONTENTS IX 5.7.3 THE CONTINUOUS PARAMETER MARKOV
CHAIN INTERPOLATION 138 5.7.4 EXAMPLES 138 5.7.5 THE REFLECTED JUMP
DIFFUSION 141 5.8 DYNAMIC PROGRAMMING EQUATIONS 141 5.8.1 OPTIMAL
STOPPING 141 5.8.2 CONTROL UNTIL EXIT FROM A COMPACT SET 144 5.8.3
REFLECTING BOUNDARY 145 5.9 CONTROLLED AND STATE DEPENDENT VARIANCE 148
COMPUTATIONAL METHODS FOR CONTROLLED MARKOV CHAINS 153 6.1 THE PROBLEM
FORMULATION 154 6.2 CLASSICAL ITERATIVE METHODS 156 6.2.1 APPROXIMATION
IN POLICY SPACE 156 6.2.2 APPROXIMATION IN VALUE SPACE 158 6.2.3
COMBINED APPROXIMATION IN POLICY SPACE AND APPROXIMATION IN VALUE SPACE
160 6.2.4 THE GAUSS-SEIDEL METHOD: PREFERRED ORDERINGS OF THE STATES 161
6.3 ERROR BOUNDS 164 6.3.1 THE JACOBI ITERATION 164 6.3.2 THE
GAUSS-SEIDEL PROCEDURE 165 6.4 ACCELERATED JACOBI AND GAUSS-SEIDEL
METHODS 166 6.4.1 THE ACCELERATED AND WEIGHTED ALGORITHMS 166 6.4.2
NUMERICAL COMPARISONS BETWEEN THE BASIC AND ACCELERATED PROCEDURES 168
6.4.3 EXAMPLE 170 6.5 DOMAIN DECOMPOSITION 171 6.6 COARSE GRID-FINE GRID
SOLUTIONS 174 6.7 A MULTIGRID METHOD 176 6.7.1 THE SMOOTHING PROPERTIES
OF THE GAUSS-SEIDEL ITERATION 176 6.7.2 A MULTIGRID METHOD 179 6.8
LINEAR PROGRAMMING 183 6.8.1 LINEAR PROGRAMMING 183 6.8.2 THE LP
FORMULATION OF THE MARKOV CHAIN CONTROL PROBLEM 186 THE ERGODIC COST
PROBLEM: FORMULATION AND ALGORITHMS 191 7.1 FORMULATION OF THE CONTROL
PROBLEM 192 7.2 A JACOBI TYPE ITERATION 196 7.3 APPROXIMATION IN POLICY
SPACE 197 7.4 NUMERICAL METHODS 199 7.5 THE CONTROL PROBLEM 201 7.6 THE
INTERPOLATED PROCESS 206 X CONTENTS 7.7 COMPUTATIONS 207 7.7.1 CONSTANT
INTERPOLATION INTERVALS 207 7.7.2 THE EQUATION FOR THE COST (5.3) IN
CENTERED FORM . . 209 7.8 BOUNDARY COSTS AND CONTROLS 213 8 HEAVY
TRAFFIC AND SINGULAR CONTROL 215 8.1 MOTIVATING EXAMPLES 216 8.1.1
EXAMPLE 1. A SIMPLE QUEUEING PROBLEM 216 8.1.2 EXAMPLE 2. A HEURISTIC
LIMIT FOR EXAMPLE 1 217 8.1.3 EXAMPLE 3. CONTROL OF ADMISSION, A
SINGULAR CONTROL PROBLEM 221 8.1.4 EXAMPLE 4. A MULTIDIMENSIONAL
QUEUEING OR PRODUC- TION SYSTEM UNDER HEAVY TRAFFIC: NO CONTROL 223
8.1.5 EXAMPLE 5. A PRODUCTION SYSTEM IN HEAVY TRAFFIC WITH IMPULSIVE
CONTROL 228 8.1.6 EXAMPLE 6. A TWO DIMENSIONAL ROUTING CONTROL PROBLEM
229 8.1.7 EXAMPLE 7 233 8.2 THE HEAVY TRAFFIC PROBLEM 234 8.2.1 THE
BASIC MODEL 234 8.2.2 THE NUMERICAL METHOD 236 8.3 SINGULAR CONTROL 240
9 WEAK CONVERGENCE AND THE CHARACTERIZATION OF PROCESSES 245 9.1 WEAK
CONVERGENCE 246 9.1.1 DEFINITIONS AND MOTIVATION 246 9.1.2 BASIC
THEOREMS OF WEAK CONVERGENCE 247 9.2 CRITERIA FOR TIGHTNESS IN D K [0,
OO) 250 9.3 CHARACTERIZATION OF PROCESSES 251 9.4 AN EXAMPLE 253 9.5
RELAXED CONTROLS 262 10 CONVERGENCE PROOFS 267 10.1 LIMIT THEOREMS 268
10.1.1 LIMIT OF A SEQUENCE OF CONTROLLED DIFFUSIONS 268 10.1.2 AN
APPROXIMATION THEOREM FOR RELAXED CONTROLS . . . 275 10.2 EXISTENCE OF
AN OPTIMAL CONTROL 276 10.3 APPROXIMATING THE OPTIMAL CONTROL 282 10.4
THE APPROXIMATING MARKOV CHAIN 286 10.4.1 APPROXIMATIONS AND
REPRESENTATIONS FOR TP H (-) .... 287 10.4.2 THE CONVERGENCE THEOREM FOR
THE INTERPOLATED CHAINS 290 10.5 CONVERGENCE OF THE COSTS 291 10.6
OPTIMAL STOPPING 296 CONTENTS XI 11 CONVERGENCE FOR REFLECTING
BOUNDARIES, SINGULAR CONTROL, AND ERGODIC COST PROBLEMS 301 11.1 THE
REFLECTING BOUNDARY PROBLEM 302 11.1.1 THE SYSTEM MODEL AND MARKOV CHAIN
APPROXIMATION 302 11.1.2 WEAK CONVERGENCE OF THE APPROXIMATING PROCESSES
. 306 11.2 THE SINGULAR CONTROL PROBLEM 315 11.3 THE ERGODIC COST
PROBLEM 320 12 FINITE TIME PROBLEMS AND NONLINEAR FILTERING 325 12.1
EXPLICIT APPROXIMATIONS: AN EXAMPLE 326 12.2 GENERAL EXPLICIT
APPROXIMATIONS 330 12.3 IMPLICIT APPROXIMATIONS: AN EXAMPLE 331 12.4
GENERAL IMPLICIT APPROXIMATIONS 333 12.5 OPTIMAL CONTROL COMPUTATIONS
335 12.6 SOLUTION METHODS * 337 12.7 NONLINEAR FILTERING 340 12.7.1
APPROXIMATION TO THE SOLUTION OF THE FOKKER-PLANCK EQUATION 340 12.7.2
THE NONLINEAR FILTERING PROBLEM: INTRODUCTION AND REPRESENTATION 341
12.7.3 THE APPROXIMATION TO THE OPTIMAL FILTER FOR X(-),Y(-) 345 13
CONTROLLED VARIANCE AND JUMPS 347 13.1 CONTROLLED VARIANCE: INTRODUCTION
348 13.1.1 INTRODUCTION 348 13.1.2 MARTINGALE MEASURES 351 13.1.3
CONVERGENCE 354 13.2 CONTROLLED JUMPS 357 13.2.1 INTRODUCTION 357 13.2.2
THE RELAXED POISSON MEASURE 361 13.2.3 OPTIMAL CONTROLS 364 13.2.4
CONVERGENCE OF THE NUMERICAL ALGORITHM 365 14 PROBLEMS FROM THE CALCULUS
OF VARIATIONS: FINITE TIME HORIZON 367 14.1 PROBLEMS WITH A CONTINUOUS
RUNNING COST 368 14.2 NUMERICAL SCHEMES AND CONVERGENCE 371 14.2.1
DESCRIPTIONS OF THE NUMERICAL SCHEMES 372 14.2.2 APPROXIMATIONS AND
PROPERTIES OF THE VALUE FUNCTION 373 14.2.3 CONVERGENCE THEOREMS 378
14.3 PROBLEMS WITH A DISCONTINUOUS RUNNING COST 384 14.3.1 DEFINITION
AND INTERPRETATION OF THE COST ON THE INTERFACE 386 14.3.2 NUMERICAL
SCHEMES AND THE PROOF OF CONVERGENCE . . 388 XII CONTENTS 15 PROBLEMS
FROM THE CALCULUS OF VARIATIONS: INFINITE TIME HORIZON 401 15.1 PROBLEMS
OF INTEREST 403 15.2 NUMERICAL SCHEMES FOR THE CASE K(X, A) KO 0 404
15.2.1 THE GENERAL APPROXIMATION 404 15.2.2 PROBLEMS WITH QUADRATIC COST
IN THE CONTROL 405 15.3 NUMERICAL SCHEMES FOR THE CASE K(X, A) 0 409
15.3.1 THE GENERAL APPROXIMATION 410 15.3.2 PROOF OF CONVERGENCE 411
15.3.3 A SHAPE FROM SHADING EXAMPLE 422 15.4 REMARKS ON IMPLEMENTATION
AND EXAMPLES 435 16 THE VISCOSITY SOLUTION APPROACH 443 16.1 DEFINITIONS
AND SOME PROPERTIES OF VISCOSITY SOLUTIONS . . . 444 16.2 NUMERICAL
SCHEMES 449 16.3 PROOF OF CONVERGENCE 453 REFERENCES 455 INDEX 467 LIST
OF SYMBOLS 473
|
| any_adam_object | 1 |
| author | Kushner, Harold J. 1933- Dupuis, Paul |
| author_GND | (DE-588)11559163X (DE-588)171353714 |
| author_facet | Kushner, Harold J. 1933- Dupuis, Paul |
| author_role | aut aut |
| author_sort | Kushner, Harold J. 1933- |
| author_variant | h j k hj hjk p d pd |
| building | Verbundindex |
| bvnumber | BV013967085 |
| callnumber-first | Q - Science |
| callnumber-label | QA402 |
| callnumber-raw | QA402.37.K87 2001 |
| callnumber-search | QA402.37.K87 2001 |
| callnumber-sort | QA 3402.37 K87 42001 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 SK 880 |
| classification_tum | MAT 605f MAT 606f |
| ctrlnum | (OCoLC)247384791 (DE-599)BVBBV013967085 |
| dewey-full | 003.76 003.7621 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003.76 003.76 21 |
| dewey-search | 003.76 003.76 21 |
| dewey-sort | 13.76 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| edition | second edition |
| format | Book |
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| id | DE-604.BV013967085 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:55:17Z |
| institution | BVB |
| isbn | 0387951393 9780387951393 9781461300076 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009559888 |
| oclc_num | 247384791 |
| open_access_boolean | |
| owner | DE-703 DE-29T DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-20 DE-521 DE-473 DE-BY-UBG DE-83 DE-11 DE-634 |
| owner_facet | DE-703 DE-29T DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-20 DE-521 DE-473 DE-BY-UBG DE-83 DE-11 DE-634 |
| physical | xii, 475 Seiten Diagramme |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Applications of mathematics |
| series2 | Applications of mathematics |
| spelling | Kushner, Harold J. 1933- (DE-588)11559163X aut Numerical methods for stochastic control problems in continuous time Harold J. Kushner ; Paul Dupuis second edition New York Springer [2001] © 2001 xii, 475 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 24 Bibliographie enthalten / Bibliography included - 3 Lehrbuch / Textbook - 28 Numerisches Verfahren / Stochastischer Prozess / Markovscher Prozess / Theorie Stochastic control theory Markov processes Numerical analysis Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Stochastische Kontrolltheorie (DE-588)4263657-7 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Stochastische Kontrolltheorie (DE-588)4263657-7 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Numerische Mathematik (DE-588)4042805-9 s 1\p DE-604 Dupuis, Paul (DE-588)171353714 aut Erscheint auch als Online-Ausgabe 978-1-4613-0007-6 Applications of mathematics 24 (DE-604)BV000895226 24 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009559888&sequence=000001&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- Dupuis, Paul Numerical methods for stochastic control problems in continuous time Applications of mathematics Bibliographie enthalten / Bibliography included - 3 Lehrbuch / Textbook - 28 Numerisches Verfahren / Stochastischer Prozess / Markovscher Prozess / Theorie Stochastic control theory Markov processes Numerical analysis Numerisches Verfahren (DE-588)4128130-5 gnd Stochastische Kontrolltheorie (DE-588)4263657-7 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4263657-7 (DE-588)4042805-9 |
| title | Numerical methods for stochastic control problems in continuous time |
| title_auth | Numerical methods for stochastic control problems in continuous time |
| title_exact_search | Numerical methods for stochastic control problems in continuous time |
| title_full | Numerical methods for stochastic control problems in continuous time Harold J. Kushner ; Paul Dupuis |
| title_fullStr | Numerical methods for stochastic control problems in continuous time Harold J. Kushner ; Paul Dupuis |
| title_full_unstemmed | Numerical methods for stochastic control problems in continuous time Harold J. Kushner ; Paul Dupuis |
| title_short | Numerical methods for stochastic control problems in continuous time |
| title_sort | numerical methods for stochastic control problems in continuous time |
| topic | Bibliographie enthalten / Bibliography included - 3 Lehrbuch / Textbook - 28 Numerisches Verfahren / Stochastischer Prozess / Markovscher Prozess / Theorie Stochastic control theory Markov processes Numerical analysis Numerisches Verfahren (DE-588)4128130-5 gnd Stochastische Kontrolltheorie (DE-588)4263657-7 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Bibliographie enthalten / Bibliography included - 3 Lehrbuch / Textbook - 28 Numerisches Verfahren / Stochastischer Prozess / Markovscher Prozess / Theorie Stochastic control theory Markov processes Numerical analysis Numerisches Verfahren Stochastische Kontrolltheorie Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009559888&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000895226 |
| work_keys_str_mv | AT kushnerharoldj numericalmethodsforstochasticcontrolproblemsincontinuoustime AT dupuispaul numericalmethodsforstochasticcontrolproblemsincontinuoustime |