The stochastic optimal control uses the differential equation of Bellman and its solution—the Bellman function. We show how the homonym function in harmonic analysis is (and how it is not) the same stochastic optimal control Bellman function. Then we present several creatures from Bellman’s Zoo: a function that proves the inverse Hölder inequality, as well as several other harmonic analysis Bel...

I Bellman, R., "On the Theory of Dynamic Programming," PROC. NATL. ACAD. Sci., 38, 716-719 (1952). 2 Bellman, R., "Some Functional Equations in the Theory of Dynamic Programming," Ibid., 39, 1077-1082 (1953). ' Bellman, R., "Bottleneck Problems and Dynamic Programming," Ibid., 39, 947-951 (1953). 4 Bellman, R., "A Problem in the Theory of Dynamic Programming," Econometrica (to appear). 6 Bellma...

The emergence in the past decade of the Bellman function method as a powerful and versatile harmonic analysis technique has been characterized by rapid theoretical development on the one hand and somewhat ad hoc, if effective, approaches to some problems on the other. From the groundbreaking applications in [NTV1, NT, NTV2], which put the method on the map, to the concerted effort at tracing it...

This morphism sends probability calculus into optimal control problems. Therefore almost of the concepts introduced in probability calculus have an optimization counterpart. The purpose of this paper is to make a presentation of known and new results of optimal control with this morphism in mind. The emphasis of this talk is i) on the trajectory point of view by opposition to the cost point of ...

Inthispaper,wesolveHamilton-Jocobi-Bellman(HJB)equationsarisinginoptimalcontrolproblems usingHomotopyPerturbationTransformMethod(HPTM).Theproposedmethodisacombinedform oftheLaplaceTransformationMethodwiththeHomotopyPerturbationMethodtoproduceahighly effectivemethodtohandlemanyproblems. ApplyingtheHPTM,solutionprocedurebecomeseasier, simplerandmorestraightforward. Someillustrativeexamplesaregive...