An Approximation Scheme for Reflected Stochastic Differential Equations

In this paper we consider the Stratonovich reflected stochastic differential equation $dX_t=\sigma(X_t)\circ dW_t+b(X_t)dt+dL_t$ in a bounded domain \O which satisfies conditions, introduced by Lions and Sznitman, which are specified below. Letting $W^N_t$ be the $N$-dyadic piecewise linear interpolation of $W_t$ what we show is that one can solve the reflected ordinary differential equation $\dot X^N_t=\sigma(X^N_t)\dot W^N_t+b(X^N_t)+\dot L^N_t$ and that the distribution of the pair $(X^N_t,L^N_t)$ converges weakly to that of $(X_t,L_t)$. Hence, what we prove is a distributional version for reflected diffusions of the famous result of Wong and Zakai. Perhaps the most valuable contribution made by our procedure derives from the representation of $\dot X^N_t$ in terms of a projection of $\dot W_t^N$. In particular, we apply our result in hand to derive some geometric properties of coupled reflected Brownian motion in certain domains, especially those properties which have been used in recent work on the "hot spots" conjecture for special domain.Comment: 26 pages, 4 figure

Blackwell-Optimal Strategies in Priority Mean-Payoff Games

We examine perfect information stochastic mean-payoff games - a class of games containing as special sub-classes the usual mean-payoff games and parity games. We show that deterministic memoryless strategies that are optimal for discounted games with state-dependent discount factors close to 1 are optimal for priority mean-payoff games establishing a strong link between these two classes

Basic Atomic Physics

Contains reports on four research projects.Joint Services Electronics Program Contract DAAL03-92-C-0001National Science Foundation Grant PHY 89-19381U.S. Navy - Office of Naval Research Grant N00014-90-J-1322National Science Foundation Grant PHY 89-21769U.S. Army - Office of Scientific Research Contract DAAL03-89-K-0082U.S. Navy - Office of Naval Research Grant N00014-89-J-1207U.S. Navy - Office of Naval Research Grant N00014-90-J-164