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Introduction to Stochastic Dynamic Programming.pdf
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Introduction to Stochastic Dynamic Programming Sheldon Ross 高清英文版
This text presents the basic theory and examines the scope of applications
of stochastic dynamic programming. Chapter I is a study of a variety of
finite-stage models, illustrating the wide range of applications of stochastic
dynamic programming. Later chapters study infinite-stage models: discounting
future returns in Chapter II, minimizing nonnegative costs in
Chapter III, maximizing nonnegative returns in Chapter IV, and maximizing
the long-run average return in Chapter V. Each of these chapters first
considers whether an optimal policy need exist—presenting counterexamples
where appropriate—and then presents methods for obtaining such
policies when they do. In addition, general areas of application are presented;
for example, optimal stopping problems are considered in Chapter
III and a variety of gambling models in Chapter IV. The final two chapters
are concerned with more specialized models. Chapter VI presents a variety
of stochastic scheduling models, and Chapter VII examines a type of
process known as a multiproject bandit.
The mathematical prerequisites for this text are relatively few. No prior
knowledge of dynamic programming is assumed and only a moderate
familiarity with probability— including the use of conditional expectation—
is necessary. I have attempted to present all proofs in as intuitive a
manner as possible. An appendix dealing with stochastic order relations,
which is needed primarily for the final two chapters, is included. Throughout
the text I use the terms increasing and nondecreasing interchangeably.
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