Much of classical and contemporary analysis stems from this source: iteration, ergodic theory, the theory of semigroups , the theory of branching processes , random transformations at fixed times and deterministic transformations at stochastic times [3, 4]. Let us now describe a dynamic programming process of discrete, deterministic type. This is an extremely important observation since it enables us to employ a type of approximation not available in classical analysis, approximation in policy space. A particular class of problems of this type involves ordinary and partial differential operators and is related both to the theory of differential inequalities inaugurated by Caplygin and Lyapunoy [15, 16], and to the modern maximum principles of partial differential equations.
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The Dawn of Dynamic Programming Richard E. Bellman (1920–1984) is best known for the invention of dynamic programming in the 1950s. During his amazingly prolific career, based primarily at The University of Southern California, he published 39 books (several of which were reprinted by Dover, including Dynamic Programming, 42809-5, 2003) and 619 papers. Professor Bellman was awarded the IEEE Medal of Honor in 1979 "for contributions to decision processes and control system theory, particularly the creation and application of dynamic programming." The IEEE citation continued: "Richard Bellman is a towering figure among the contributors to modern control theory and systems analysis.
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