Continuous time Markov decision processes: theory and applications
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
[2009]
|
| Series: | Stochastic modelling and applied probability
62 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvii, 231 Seite |
| ISBN: | 9783642025464 9783642025471 |
Staff View
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Record in the Search Index
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| adam_text | X CONTENTS INTRODUCTION AND SUMMARY 1 1.1 INTRODUCTION 1 1.2
PRELIMINARY EXAMPLES 1 1.3 SUMMARY OF THE FOLLOWING CHAPTERS 6
CONTINUOUS-TIME MARKOV DECISION PROCESSES 9 2.1 INTRODUCTION 9 2.2 THE
CONTROL MODEL 10 2.3 CONTINUOUS-TIME MARKOV DECISION PROCESSES 13 2.4
BASIC OPTIMALITY CRITERIA 16 AVERAGE OPTIMALITY FOR FINITE MODELS 19 3.1
INTRODUCTION 19 3.2 N-BIAS OPTIMALITY CRITERIA 20 3.3 DIFFERENCE
FORMULAS OF N-BIASES 23 3.4 CHARACTERIZATION OF N-BIAS POLICIES 29 3.5
COMPUTATION OF N-BIAS OPTIMAL POLICIES 36 3.5.1 THE POLICY ITERATION
ALGORITHM FOR AVERAGE OPTIMALITY . . . 36 3.5.2 THE 0-BIAS POLICY
ITERATION ALGORITHM 39 3.5.3 N-BIAS POLICY ITERATION ALGORITHMS 43 3.6
THE LINEAR PROGRAMMING APPROACH 46 3.6.1 LINEAR PROGRAMMING FOR ERGODIC
MODELS 46 3.6.2 LINEAR PROGRAMMING FOR MULTICHAIN MODELS 49 3.7 NOTES 52
DISCOUNT OPTIMALITY FOR NONNEGATIVE COSTS 55 4.1 INTRODUCTION 55 4.2 THE
NONNEGATIVE MODEL 55 4.3 PRELIMINARIES 56 4.4 THE DISCOUNTED COST
OPTIMALITY EQUATION 60 4.5 EXISTENCE OF OPTIMAL POLICIES 63 4.6
APPROXIMATION RESULTS 63 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/994394683 DIGITALISIERT DURCH X CONTENTS 4.7 THE POLICY
ITERATION APPROACH 66 4.8 EXAMPLES 68 4.9 NOTES 69 5 AVERAGE OPTIMALITY
FOR NONNEGATIVE COSTS 71 5.1 INTRODUCTION 71 5.2 THE AVERAGE-COST
CRITERION 72 5.3 THE MINIMUM NONNEGATIVE SOLUTION APPROACH 73 5.4 THE
AVERAGE-COST OPTIMALITY INEQUALITY 76 5.5 THE AVERAGE-COST OPTIMALITY
EQUATION 80 5.6 EXAMPLES 81 5.7 NOTES 84 6 DISCOUNT OPTIMALITY FOR
UNBOUNDED REWARDS 87 6.1 INTRODUCTION 87 6.2 THE DISCOUNTED-REWARD
OPTIMALITY EQUATION 89 6.3 DISCOUNT OPTIMAL STATIONARY POLICIES 95 6.4 A
VALUE ITERATION ALGORITHM 98 6.5 EXAMPLES 98 6.6 NOTES 102 7 AVERAGE
OPTIMALITY FOR UNBOUNDED REWARDS 105 7.1 INTRODUCTION 105 7.2
EXPONENTIAL ERGODICITY CONDITIONS 106 7.3 THE EXISTENCE OF AR OPTIMAL
POLICIES 109 7.4 THE POLICY ITERATION ALGORITHM 113 7.5 EXAMPLES 119 7.6
NOTES 124 8 AVERAGE OPTIMALITY FOR PATHWISE REWARDS 127 8.1 INTRODUCTION
127 8.2 THE OPTIMAL CONTROL PROBLEM 129 8.3 OPTIMALITY CONDITIONS AND
PRELIMINARIES 129 8.4 THE EXISTENCE OF PAR OPTIMAL POLICIES 131 8.5
POLICY AND VALUE ITERATION ALGORITHMS 138 8.6 AN EXAMPLE 139 8.7 NOTES
142 9 ADVANCED OPTIMALITY CRITERIA 143 9.1 BIAS AND WEAKLY OVERTAKING
OPTIMALITY 143 9. CONTENTS XI 10.2 PRELIMINARIES 164 10.3 COMPUTATION OF
THE AVERAGE VARIANCE 164 10.4 VARIANCE MINIMIZATION 170 10.5 EXAMPLES
171 10.6 NOTES 173 11 CONSTRAINED OPTIMALITY FOR DISCOUNT CRITERIA 175
11.1 THE MODEL WITH A CONSTRAINT 175 11.2 PRELIMINARIES 177 11.3 PROOF
OF THEOREM 11.4 182 11.4 AN EXAMPLE 184 11.5 NOTES 186 12 CONSTRAINED
OPTIMALITY FOR AVERAGE CRITERIA 187 12.1 AVERAGE OPTIMALITY WITH A
CONSTRAINT 187 12.2 PRELIMINARIES 188 12.3 PROOF OF THEOREM 12.4 192
12.4 AN EXAMPLE 192 12.5 NOTES 194 A 195 A.I LIMIT THEOREMS 195 A.2
RESULTS FROM MEASURE THEORY 197 * 203 B.I CONTINUOUS-TIME MARKOV CHAINS
203 B.2 STATIONARY DISTRIBUTIONS AND ERGODICITY 206 C 209 C.I THE
CONSTRUCTION OF TRANSITION FUNCTIONS 209 C.2 ERGODICITY BASED ON THE
SS-MATRIX 214 C.3 DYNKIN S FORMULA 218 REFERENCES 221 INDEX 229
|
| any_adam_object | 1 |
| author | Guo, Xianping Hernández-Lerma, Onésimo 1946- |
| author_GND | (DE-588)140541888 (DE-588)111571081 |
| author_facet | Guo, Xianping Hernández-Lerma, Onésimo 1946- |
| author_role | aut aut |
| author_sort | Guo, Xianping |
| author_variant | x g xg o h l ohl |
| building | Verbundindex |
| bvnumber | BV035683332 |
| classification_rvk | SK 620 SK 820 |
| classification_tum | MAT 607f MAT 900f |
| ctrlnum | (OCoLC)502397459 (DE-599)DNB994394683 |
| dewey-full | 519.233 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.233 |
| dewey-search | 519.233 |
| dewey-sort | 3519.233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035683332 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:43:20Z |
| institution | BVB |
| isbn | 9783642025464 9783642025471 |
| language | English |
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| physical | xvii, 231 Seite |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Stochastic modelling and applied probability |
| series2 | Stochastic modelling and applied probability |
| spelling | Guo, Xianping (DE-588)140541888 aut Continuous time Markov decision processes theory and applications Xianping Guo ; Onésimo Hernández-Lerma Continuous-time Markov decision processes Berlin [u.a.] Springer [2009] © 2009 xvii, 231 Seite txt rdacontent n rdamedia nc rdacarrier Stochastic modelling and applied probability 62 Markov-Entscheidungsprozess (DE-588)4168927-6 gnd rswk-swf Markov-Entscheidungsprozess (DE-588)4168927-6 s DE-604 Hernández-Lerma, Onésimo 1946- (DE-588)111571081 aut Erscheint auch als Online-Ausgabe 978-3-642-02547-1 Stochastic modelling and applied probability 62 (DE-604)BV019623501 62 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017737558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Guo, Xianping Hernández-Lerma, Onésimo 1946- Continuous time Markov decision processes theory and applications Stochastic modelling and applied probability Markov-Entscheidungsprozess (DE-588)4168927-6 gnd |
| subject_GND | (DE-588)4168927-6 |
| title | Continuous time Markov decision processes theory and applications |
| title_alt | Continuous-time Markov decision processes |
| title_auth | Continuous time Markov decision processes theory and applications |
| title_exact_search | Continuous time Markov decision processes theory and applications |
| title_full | Continuous time Markov decision processes theory and applications Xianping Guo ; Onésimo Hernández-Lerma |
| title_fullStr | Continuous time Markov decision processes theory and applications Xianping Guo ; Onésimo Hernández-Lerma |
| title_full_unstemmed | Continuous time Markov decision processes theory and applications Xianping Guo ; Onésimo Hernández-Lerma |
| title_short | Continuous time Markov decision processes |
| title_sort | continuous time markov decision processes theory and applications |
| title_sub | theory and applications |
| topic | Markov-Entscheidungsprozess (DE-588)4168927-6 gnd |
| topic_facet | Markov-Entscheidungsprozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017737558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019623501 |
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