Numerical Methods for Stochastic Control Problems in Continuous TimeSpringer Science & Business Media, 2001 - 475 sider Changes in the second edition. The second edition differs from the first in that there is a full development of problems where the variance of the diffusion term and the jump distribution can be controlled. Also, a great deal of new material concerning deterministic problems has been added, including very efficient algorithms for a class of problems of wide current interest. This book is concerned with numerical methods for stochastic control and optimal stochastic control problems. The random process models of the controlled or uncontrolled stochastic systems are either diffusions or jump diffusions. Stochastic control is a very active area of research and new problem formulations and sometimes surprising applications appear regu larly. We have chosen forms of the models which cover the great bulk of the formulations of the continuous time stochastic control problems which have appeared to date. The standard formats are covered, but much emphasis is given to the newer and less well known formulations. The controlled process might be either stopped or absorbed on leaving a constraint set or upon first hitting a target set, or it might be reflected or "projected" from the boundary of a constraining set. In some of the more recent applications of the reflecting boundary problem, for example the so-called heavy traffic approximation problems, the directions of reflection are actually discontin uous. In general, the control might be representable as a bounded function or it might be of the so-called impulsive or singular control types. |
Innhold
II | 7 |
III | 8 |
IV | 9 |
V | 14 |
VI | 21 |
VII | 28 |
VIII | 31 |
X | 32 |
LII | 204 |
LIII | 222 |
LIV | 233 |
LVI | 234 |
LVII | 238 |
LVIII | 239 |
LIX | 241 |
LX | 250 |
XI | 38 |
XII | 44 |
XIII | 49 |
XV | 51 |
XVI | 53 |
XVII | 56 |
XVIII | 58 |
XIX | 62 |
XX | 64 |
XXI | 69 |
XXII | 73 |
XXIII | 75 |
XXIV | 85 |
XXV | 94 |
XXVI | 101 |
XXVII | 110 |
XXVIII | 115 |
XXIX | 120 |
XXX | 129 |
XXXI | 136 |
XXXII | 141 |
XXXIV | 142 |
XXXV | 144 |
XXXVI | 154 |
XXXVII | 159 |
XXXVIII | 162 |
XXXIX | 164 |
XL | 171 |
XLI | 179 |
XLII | 180 |
XLIII | 184 |
XLIV | 185 |
XLV | 187 |
XLVI | 189 |
XLVII | 194 |
XLVIII | 195 |
XLIX | 201 |
L | 203 |
LXI | 255 |
LXII | 256 |
LXIII | 264 |
LXIV | 270 |
LXV | 274 |
LXVI | 284 |
LXVII | 289 |
LXIX | 290 |
LXX | 303 |
LXXI | 308 |
LXXII | 313 |
LXXIV | 314 |
LXXV | 318 |
LXXVI | 319 |
LXXVII | 321 |
LXXVIII | 323 |
LXXIX | 325 |
LXXX | 328 |
LXXXI | 335 |
LXXXIII | 336 |
LXXXIV | 345 |
LXXXV | 355 |
LXXXVII | 356 |
LXXXVIII | 359 |
LXXXIX | 372 |
XC | 389 |
XCII | 391 |
XCIII | 392 |
XCIV | 397 |
XCV | 423 |
XCVI | 431 |
XCVIII | 432 |
XCIX | 437 |
C | 440 |
CI | 443 |
455 | |
CIII | 461 |
Andre utgaver - Vis alle
Numerical Methods for Stochastic Control Problems in Continuous Time Harold Kushner,Paul G. Dupuis Begrenset visning - 2013 |
Numerical Methods for Stochastic Control Problems in Continuous Time Harold Kushner,Paul G. Dupuis Ingen forhåndsvisning tilgjengelig - 2013 |
Numerical Methods for Stochastic Control Problems in Continuous Time Harold Kushner,Paul G. Dupuis Ingen forhåndsvisning tilgjengelig - 2013 |
Vanlige uttrykk og setninger
admissible control algorithm analogous approximating chain approximating Markov chain assume assumptions Bellman equation boundary condition bounded calculus of variations Chapter component computational consider continuous function continuous parameter control problem controlled Markov chain controlled process convergent subsequence converges weakly cost function da)ds dads defined definition denote discounted discussed dynamic programming equation example feedback control Ft-Wiener process Gauss-Seidel given grid implies infimum initial condition interpolation interval iteration jump diffusion lim inf lim sup locally consistent Markov chain approximation Markov property martingale matrix minimizing notation optimal control ph(x points Poisson measure probability space procedure properties reflected diffusion reflecting boundary reflection directions relaxed control representation running cost satisfies Section sequence Skorokhod solution stochastic differential equation Subsection Suppose transition probabilities uniform integrability unique vector Vh(x weak convergence weak sense Wh(x Wiener process zero
Referanser til denne boken
Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner Ingen forhåndsvisning tilgjengelig - 2006 |
Stochastic Approximation and Recursive Algorithms and Applications Harold Kushner,G. George Yin Ingen forhåndsvisning tilgjengelig - 2003 |