The paper presents sufficient conditions of predictability for continuous time processes in deterministic setting. We found that processes with exponential decay on energy for higher frequencies are predictable in some weak sense on some finite time horizon defined by the rate of decay. Moreover, this predictability can be achieved uniformly over classes of processes. Some explicit formulas for...

In this chapter we study Markov decision processes (MDPs) with nite state and action spaces. This is the classical theory developed since the end of the fties. We consider nite and in nite horizon models. For the nite horizon model the utility function of the total expected reward is commonly used. For the in nite horizon the utility function is less obvious. We consider several criteria: total...

Supersymmetry of five dimensional string solutions is examined in the context of gauged D = 5, N = 2 supergravity coupled to abelian vector multiplets. We find magnetic black strings preserving one quarter of supersymmetry and approaching the half-supersymmetric product space AdS3 × H near the event horizon. The solutions thus exhibit the phenomenon of supersymmetry enhancement near the horizon...

In this paper we discuss the question of whether the entropy of cosmological horizon in some asymptotically de Sitter spaces can be described by the Cardy-Verlinde formula, which is supposed to be an entropy formula of conformal field theory in any dimension. For the Schwarzschild-de Sitter solution, although the gravitational mass is always negative (in the sense of the prescription in hep-th/...

In this paper we derive stabilization conditions for the class of PWA systems using the linear matrix inequality (LMI) framework. We consider the class of piecewise affine feedback controllers and the class of piecewise quadratic Lyapunov functions that guarantee stability of the closed-loop system. We take into account the piecewise structure of the system and therefore the matrix inequalities...

We study the problem of receding horizon control for stochastic discrete-time systems with bounded control inputs and incomplete state information. Given a suitable choice of causal control policies, we first present a slight extension of the Kalman filter to estimate the state optimally in mean-square sense. We then show how to augment the underlying optimization problem with a negative drift-...

The (2k + 2)-dimensional Einstein-Yang-Mills equations for gauge group SO(2k) (or SU(2) for k = 2 and SU(3) for k = 3) are shown to admit a family of spherically-symmetric magnetic monopole solutions characterized by a mass m and a magnetic-type charge, the k = 1 case being the Reissner-Nordstrom black hole. The k = 2 case yields a family of self-gravitating Yang monopoles, and for k = 4 we fin...

An extensive literature documents heterogeneity in the delay of stock-price reaction to systematic shocks, implying that relevant asset risk depends on investment horizon. We study pricing of common risk factors across investment horizons. We …nd that liquidity risk is priced over short horizons and market risk is priced over intermediate horizons. Value/growth risk is priced over long horizons...