HJB equations in infinite dimensions under weak regularizing properties

Stochastic Optimal Control in Infinite Dimensions: Dynamic Programming and HJB Equations

Stochastic Differential Equations in Infinite Dimensions

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Nonlinear HJB Equations

This paper is concerned with the standard finite element approximation of HamiltonJacobi-Bellman Equations (HJB) with nonlinear source terms. Under a realistic condition on the nonlinearity, we characterize the discrete solution as a fixed point of a contraction. As a result of this, we also derive a sharp L∞error estimate of the approximation. Mathematics Subject Classification: Primary 35F21;...

Weak Partition Properties for Infinite Cardinals. I

Partition properties are perhaps the most fruitful of the various methods for defining and discussing large cardinals in set theory. In this paper we weaken in a natural way the most well known of these partition properties and examine the extent to which the cardinals defined remain "large." 1. 1.1. An area of set theory which has come under a great deal of study recently is that concerned wit...

Weak Covering Properties and Infinite Games

We investigate game-theoretic properties of selection principles related to weaker forms of the Menger and Rothberger properties. For appropriate spaces some of these selection principles are characterized in terms of a corresponding game. We use generic extensions by Cohen reals to illustrate the necessity of some of the hypotheses in our theorems.