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Dynamic Programming Equations

  • Harold J. Kushner
  • Paul Dupuis
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 24)

Abstract

In this chapter we define many of the standard control problems whose numerical solutions will concern us in the subsequent chapters. Other, less familiar control problems will be discussed separately in later chapters. We will first define cost functional for uncontrolled processes, and then formally discuss the partial differential equations which they satisfy. Then the cost functional for the controlled problems will be stated and the partial differential equations for the optimal cost formally derived. These partial differential equations are generally known as Bellman equations or dynamic programming equations. The main tool in the derivations is Ito’s formula.

Keywords

Average Cost Regular Point Optimal Cost Admissible Control Bellman Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Harold J. Kushner
    • 1
  • Paul Dupuis
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

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