Coverart for item
The Resource Controlled Markov processes and viscosity solutions, Wendell H. Fleming, H. Mete Soner

Controlled Markov processes and viscosity solutions, Wendell H. Fleming, H. Mete Soner

Label
Controlled Markov processes and viscosity solutions
Title
Controlled Markov processes and viscosity solutions
Statement of responsibility
Wendell H. Fleming, H. Mete Soner
Creator
Contributor
Subject
Language
eng
http://library.link/vocab/creatorDate
1928-
http://library.link/vocab/creatorName
Fleming, Wendell H.
Index
index present
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorName
Soner, H. Mete
Series statement
Applications of mathematics
Series volume
25
http://library.link/vocab/subjectName
  • Markov processes
  • Stochastic control theory
  • Viscosity solutions
Label
Controlled Markov processes and viscosity solutions, Wendell H. Fleming, H. Mete Soner
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. [409]-424) and index
Contents
  • Preface
  • Notation
  • I.
  • Deterministic Optimal Control.
  • p. 1
  • I.2.
  • Examples.
  • p. 2
  • I.3.
  • Finite time horizon problems.
  • p. 5
  • I.4.
  • Dynamic programming principle.
  • p. 9
  • I.5.
  • Dynamic programming equation.
  • p. 11
  • I.6.
  • Dynamic programming and Pontryagin's principle.
  • p. 18
  • I.7.
  • Discounted cost with infinite horizon.
  • p. 23
  • I.8.
  • Calculus of variations I.
  • p. 32
  • I.9.
  • Calculus of variations II.
  • p. 37
  • I.10.
  • Generalized solutions to Hamilton-Jacobi equations.
  • p. 43
  • II.
  • Viscosity Solutions.
  • p. 53
  • II.2.
  • Examples.
  • p. 56
  • II.3.
  • abstract dynamic programming principle.
  • p. 58
  • II.4.
  • Definition.
  • p. 64
  • II.5.
  • Dynamic programming and viscosity property.
  • p. 68
  • II.6.
  • Properties of viscosity solutions.
  • p. 70
  • II.7.
  • Deterministic optimal control and viscosity solutions.
  • p. 75
  • II.8.
  • Viscosity solutions: First-order case.
  • p. 79
  • II.9.
  • Uniqueness: First-order case.
  • p. 85
  • II.10.
  • Continuity of the value function.
  • p. 95
  • II.11.
  • Discounted cost with infinite horizon.
  • p. 99
  • II.12.
  • State constraint.
  • p. 101
  • II.13.
  • Discussion of boundary conditions.
  • p. 106
  • II.14.
  • Uniqueness: First-order case.
  • p. 108
  • II.15.
  • Pontryagin's maximum principle.
  • p. 109
  • II.16.
  • Unbounded control set U.
  • p. 111
  • III.
  • Optimal Control of Markov Processes: Classical Solutions.
  • p. 125
  • III.2.
  • Markov processes and their evolution operators.
  • p. 126
  • III.3.
  • Autonomous (time-homogeneous) Markov processes.
  • p. 129
  • III.4.
  • Classes of Markov processes.
  • p. 131
  • III.5.
  • Markov diffusion processes on [actual symbol not reproducible] stochastic differential equations.
  • p. 133
  • III.6.
  • Controlled Markov processes.
  • p. 136
  • III.7.
  • Dynamic programming: Formal description.
  • p. 137
  • III.8.
  • Verification Theorem; finite time horizon.
  • p. 140
  • III.9.
  • Infinite time-horizon.
  • p. 145
  • III.10.
  • Viscosity solutions.
  • p. 151
  • IV.
  • Controlled Markov Diffusions in [actual symbol not reproducible].
  • p. 157
  • IV.2.
  • Finite time horizon problem.
  • p. 158
  • IV.3.
  • Hamilton-Jacobi-Bellman PDE.
  • p. 161
  • IV.4.
  • Uniformly parabolic case.
  • p. 167
  • IV.5.
  • Infinite time horizon.
  • p. 171
  • IV.6.
  • Fixed finite time horizon problem: Preliminary estimates.
  • p. 177
  • IV.7.
  • Dynamic programming principle.
  • p. 182
  • IV.8.
  • Estimates for first-order difference quotients.
  • p. 189
  • IV.9.
  • Estimates for second-order difference quotients.
  • p. 193
  • IV.10.
  • Generalized subsolutions and solutions.
  • p. 197
  • IV.11.
  • Stochastic calculus of variations.
  • p. 205
  • V.
  • Viscosity Solutions: Second-Order Case.
  • p. 213
  • V.2.
  • Dynamic programming principle.
  • p. 214
  • V.3.
  • Viscosity property.
  • p. 219
  • V.4.
  • equivalent formulation.
  • p. 223
  • V.5.
  • Jensen's maximum principle.
  • p. 227
  • V.6.
  • Ishii's lemma.
  • p. 237
  • V.7.
  • Semiconvex, concave approximations.
  • p. 240
  • V.8.
  • Comparison.
  • p. 243
  • V.9.
  • Viscosity solutions in Q[subscript 0].
  • p. 247
  • VI.
  • Logarithmic Transformations.
  • p. 253
  • VI.2.
  • Nondegenerate diffusions in [actual symbol not reproducible].
  • p. 254
  • VI.3.
  • Locally optimal Markov policies.
  • p. 259
  • VI.4.
  • Conditioned Markov diffusions.
  • p. 262
  • VI.5.
  • exit problem.
  • p. 265
  • VI.6.
  • Small noise limits I.
  • p. 267
  • VI.7.
  • Small noise limits II: Asymptotic series.
  • p. 271
  • VI.8.
  • Logarithmic transformations for Markov processes.
  • p. 275
  • VII.
  • Singular Perturbations.
  • p. 281
  • VII.2.
  • Examples.
  • p. 283
  • VII.3.
  • Barles and Perthame procedure.
  • p. 285
  • VII.4.
  • Discontinuous viscosity solutions.
  • p. 287
  • VII.5.
  • Terminal condition.
  • p. 289
  • VII.6.
  • Boundary condition.
  • p. 291
  • VII.7.
  • Convergence.
  • p. 292
  • VII.8.
  • Comparison.
  • p. 293
  • VII.9.
  • Vanishing viscosity.
  • p. 301
  • VII.10.
  • Large deviations for exit probabilities.
  • p. 303
  • VIII.
  • Singular Stochastic Control.
  • p. 315
  • VIII.2.
  • Formal discussion.
  • p. 316
  • VIII.3.
  • Singular stochastic control.
  • p. 318
  • VIII.4.
  • Verification theorem.
  • p. 321
  • VIII.5.
  • Viscosity solutions.
  • p. 333
  • VIII.6.
  • Portfolio selection with transaction costs.
  • p. 339
  • VIII.7.
  • Optimal investment/transaction policy.
  • p. 342
  • VIII.8.
  • Finite fuel problem.
  • p. 359
  • IX.
  • Finite-Difference Numerical Approximations.
  • p. 363
  • IX.2.
  • Controlled discrete-time Markov chains.
  • p. 364
  • IX.3.
  • Finite-difference approximations to HJB equations.
  • p. 366
  • IX.4.
  • Convergence of finite-difference approximations I.
  • p. 374
  • IX.5.
  • Convergence of finite difference approximations II.
  • p. 379
  • Appendix A. Duality Relationships.
  • p. 389
  • Appendix B. Dynkin's Formula for Random Evolutions with Markov Chain Parameters.
  • p. 391
  • Appendix C. Extension of Lipschitz Continuous Functions; Smoothing.
  • p. 393
  • Appendix D. Stochastic Differential Equations: Random Coefficients.
  • p. 397
  • Appendix E. A Result of Alexandrov.
  • p. 403
  • References.
  • p. 409
  • Index.
  • p. 425
Control code
l80092031619
Dimensions
25 cm.
Extent
xv, 428 p.
Isbn
9780387979274
Lccn
lc92031619
Label
Controlled Markov processes and viscosity solutions, Wendell H. Fleming, H. Mete Soner
Publication
Bibliography note
Includes bibliographical references (p. [409]-424) and index
Contents
  • Preface
  • Notation
  • I.
  • Deterministic Optimal Control.
  • p. 1
  • I.2.
  • Examples.
  • p. 2
  • I.3.
  • Finite time horizon problems.
  • p. 5
  • I.4.
  • Dynamic programming principle.
  • p. 9
  • I.5.
  • Dynamic programming equation.
  • p. 11
  • I.6.
  • Dynamic programming and Pontryagin's principle.
  • p. 18
  • I.7.
  • Discounted cost with infinite horizon.
  • p. 23
  • I.8.
  • Calculus of variations I.
  • p. 32
  • I.9.
  • Calculus of variations II.
  • p. 37
  • I.10.
  • Generalized solutions to Hamilton-Jacobi equations.
  • p. 43
  • II.
  • Viscosity Solutions.
  • p. 53
  • II.2.
  • Examples.
  • p. 56
  • II.3.
  • abstract dynamic programming principle.
  • p. 58
  • II.4.
  • Definition.
  • p. 64
  • II.5.
  • Dynamic programming and viscosity property.
  • p. 68
  • II.6.
  • Properties of viscosity solutions.
  • p. 70
  • II.7.
  • Deterministic optimal control and viscosity solutions.
  • p. 75
  • II.8.
  • Viscosity solutions: First-order case.
  • p. 79
  • II.9.
  • Uniqueness: First-order case.
  • p. 85
  • II.10.
  • Continuity of the value function.
  • p. 95
  • II.11.
  • Discounted cost with infinite horizon.
  • p. 99
  • II.12.
  • State constraint.
  • p. 101
  • II.13.
  • Discussion of boundary conditions.
  • p. 106
  • II.14.
  • Uniqueness: First-order case.
  • p. 108
  • II.15.
  • Pontryagin's maximum principle.
  • p. 109
  • II.16.
  • Unbounded control set U.
  • p. 111
  • III.
  • Optimal Control of Markov Processes: Classical Solutions.
  • p. 125
  • III.2.
  • Markov processes and their evolution operators.
  • p. 126
  • III.3.
  • Autonomous (time-homogeneous) Markov processes.
  • p. 129
  • III.4.
  • Classes of Markov processes.
  • p. 131
  • III.5.
  • Markov diffusion processes on [actual symbol not reproducible] stochastic differential equations.
  • p. 133
  • III.6.
  • Controlled Markov processes.
  • p. 136
  • III.7.
  • Dynamic programming: Formal description.
  • p. 137
  • III.8.
  • Verification Theorem; finite time horizon.
  • p. 140
  • III.9.
  • Infinite time-horizon.
  • p. 145
  • III.10.
  • Viscosity solutions.
  • p. 151
  • IV.
  • Controlled Markov Diffusions in [actual symbol not reproducible].
  • p. 157
  • IV.2.
  • Finite time horizon problem.
  • p. 158
  • IV.3.
  • Hamilton-Jacobi-Bellman PDE.
  • p. 161
  • IV.4.
  • Uniformly parabolic case.
  • p. 167
  • IV.5.
  • Infinite time horizon.
  • p. 171
  • IV.6.
  • Fixed finite time horizon problem: Preliminary estimates.
  • p. 177
  • IV.7.
  • Dynamic programming principle.
  • p. 182
  • IV.8.
  • Estimates for first-order difference quotients.
  • p. 189
  • IV.9.
  • Estimates for second-order difference quotients.
  • p. 193
  • IV.10.
  • Generalized subsolutions and solutions.
  • p. 197
  • IV.11.
  • Stochastic calculus of variations.
  • p. 205
  • V.
  • Viscosity Solutions: Second-Order Case.
  • p. 213
  • V.2.
  • Dynamic programming principle.
  • p. 214
  • V.3.
  • Viscosity property.
  • p. 219
  • V.4.
  • equivalent formulation.
  • p. 223
  • V.5.
  • Jensen's maximum principle.
  • p. 227
  • V.6.
  • Ishii's lemma.
  • p. 237
  • V.7.
  • Semiconvex, concave approximations.
  • p. 240
  • V.8.
  • Comparison.
  • p. 243
  • V.9.
  • Viscosity solutions in Q[subscript 0].
  • p. 247
  • VI.
  • Logarithmic Transformations.
  • p. 253
  • VI.2.
  • Nondegenerate diffusions in [actual symbol not reproducible].
  • p. 254
  • VI.3.
  • Locally optimal Markov policies.
  • p. 259
  • VI.4.
  • Conditioned Markov diffusions.
  • p. 262
  • VI.5.
  • exit problem.
  • p. 265
  • VI.6.
  • Small noise limits I.
  • p. 267
  • VI.7.
  • Small noise limits II: Asymptotic series.
  • p. 271
  • VI.8.
  • Logarithmic transformations for Markov processes.
  • p. 275
  • VII.
  • Singular Perturbations.
  • p. 281
  • VII.2.
  • Examples.
  • p. 283
  • VII.3.
  • Barles and Perthame procedure.
  • p. 285
  • VII.4.
  • Discontinuous viscosity solutions.
  • p. 287
  • VII.5.
  • Terminal condition.
  • p. 289
  • VII.6.
  • Boundary condition.
  • p. 291
  • VII.7.
  • Convergence.
  • p. 292
  • VII.8.
  • Comparison.
  • p. 293
  • VII.9.
  • Vanishing viscosity.
  • p. 301
  • VII.10.
  • Large deviations for exit probabilities.
  • p. 303
  • VIII.
  • Singular Stochastic Control.
  • p. 315
  • VIII.2.
  • Formal discussion.
  • p. 316
  • VIII.3.
  • Singular stochastic control.
  • p. 318
  • VIII.4.
  • Verification theorem.
  • p. 321
  • VIII.5.
  • Viscosity solutions.
  • p. 333
  • VIII.6.
  • Portfolio selection with transaction costs.
  • p. 339
  • VIII.7.
  • Optimal investment/transaction policy.
  • p. 342
  • VIII.8.
  • Finite fuel problem.
  • p. 359
  • IX.
  • Finite-Difference Numerical Approximations.
  • p. 363
  • IX.2.
  • Controlled discrete-time Markov chains.
  • p. 364
  • IX.3.
  • Finite-difference approximations to HJB equations.
  • p. 366
  • IX.4.
  • Convergence of finite-difference approximations I.
  • p. 374
  • IX.5.
  • Convergence of finite difference approximations II.
  • p. 379
  • Appendix A. Duality Relationships.
  • p. 389
  • Appendix B. Dynkin's Formula for Random Evolutions with Markov Chain Parameters.
  • p. 391
  • Appendix C. Extension of Lipschitz Continuous Functions; Smoothing.
  • p. 393
  • Appendix D. Stochastic Differential Equations: Random Coefficients.
  • p. 397
  • Appendix E. A Result of Alexandrov.
  • p. 403
  • References.
  • p. 409
  • Index.
  • p. 425
Control code
l80092031619
Dimensions
25 cm.
Extent
xv, 428 p.
Isbn
9780387979274
Lccn
lc92031619

Library Locations

    • Harold Cohen LibraryBorrow it
      Ashton Street, Liverpool, L69 3DA, GB
      53.418074 -2.967913
Processing Feedback ...