rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Controlled Markov Processes and Viscosity Solutions
  name:
    name part: Fleming, Wendell H.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Soner, H.M.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2006
    edition: Second Edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVII, 429 p. online resource.
  abstract: This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. Stochastic control problems are treated using the dynamic programming approach. The authors approach stochastic control problems by the method of dynamic programming. The fundamental equation of dynamic programming is a nonlinear evolution equation for the value function. For controlled Markov diffusion processes, this becomes a nonlinear partial differential equation of second order, called a Hamilton-Jacobi-Bellman (HJB) equation. Typically, the value function is not smooth enough to satisfy the HJB equation in a classical sense. Viscosity solutions provide framework in which to study HJB equations, and to prove continuous dependence of solutions on problem data. The theory is illustrated by applications from engineering, management science, and financial economics. In this second edition, new material on applications to mathematical finance has been added. Concise introductions to risk-sensitive control theory, nonlinear H-infinity control and differential games are also included. Review of the earlier edition: "This book is highly recommended to anyone who wishes to learn the dinamic principle applied to optimal stochastic control for diffusion processes. Without any doubt, this is a fine book and most likely it is going to become a classic on the area... ." SIAM Review, 1994.
  table of contents: Deterministic Optimal Control -- Viscosity Solutions -- Optimal Control of Markov Processes: Classical Solutions -- Controlled Markov Diffusions in ?n -- Viscosity Solutions: Second-Order Case -- Logarithmic Transformations and Risk Sensitivity -- Singular Perturbations -- Singular Stochastic Control -- Finite Difference Numerical Approximations -- Applications to Finance -- Differential Games.
  note: by Wendell H. Fleming, H.M. Soner.
  subject:
    topic: Mathematics
  subject:
    topic: Operations research
  subject:
    topic: Decision making
  subject:
    topic: Economics, Mathematical
  subject:
    topic: System theory
  subject:
    topic: Probabilities
  subject:
    topic: Control engineering
  subject:
    topic: Robotics
  subject:
    topic: Mechatronics
  subject:
    topic: Mathematics
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Systems Theory, Control
  subject:
    topic: Control, Robotics, Mechatronics
  subject:
    topic: Operation Research/Decision Theory
  subject:
    topic: Quantitative Finance
  classification: QA273.A1-274.9
  classification: QA274-274.9
  classification: 519.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Stochastic Modelling and Applied Probability, 25
  identifier: 9780387310718
  identifier: http://dx.doi.org/10.1007/0-387-31071-1
  record info:
    record creation date: 100301
    record change date: 20151204152944.0
    record identifier: 978-0-387-31071-8