This paper is concerned with a stochastic linear-quadratic optimal control problem in finite time horizon, where the coefficients of system are allowed to be random, and weighting matrices cost functional random indefinite. It shown, Hilbert space approach, that for existence an open-loop control, convexity (with respect control) necessary; uniform convexity, which slightly stronger, turns out ...

We characterize the open sets in the sphere that are geodesically convex in any containing domain with respect to various conformal metrics.

Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...

In this paper we are interested in examining the geometry of a bounded convex function over a Banach space via its subdiierential mapping. We will consider two concepts. The rst is the single valuedness and continuity of the subdiierential mapping, and the second is the single valuedness and the continuity of the \inverse" of this mapping. The smoothness of f is important for the rst concept as...

Given a sample of n independant and identically distributed random vectors drawn from a density f we study two ways of testing the convexity of the support of the density. The first one requires the hypothesis that f is uniform on its support. Two statitistics are proposed, one to test non-convexity due to the boundary, the other one to detect non convexity due to the existance of a hole. p-val...

We study convexity properties of the Rényi entropy as function $\alpha >0$ on finite alphabets. also describe robustness alphabets, and it turns out that rate respective convergence depends initial alphabet. establish disturbed when distribution is uniform but number events increases to ? prove limit binomial equal Poisson distribution.

We investigate the norm of sums of independent vector-valued random variables in noncommutative Lp spaces. This allows us to obtain a uniform family of complete embeddings of the Schatten class S q in Sp(lmq ) with optimal order m ∼ n. Using these embeddings we show the surprising fact that the sharp type (cotype) index in the sense of operator spaces for Lp[0, 1] is min(p, p) (max(p, p)). Simi...

In this paper, we consider graphon particle systems with heterogeneous mean-field type interactions and the associated finite approximations. Under suitable growth (resp. convexity) assumptions, obtain uniform-in-time concentration estimates, over infinite) time horizon, for Wasserstein distance between empirical measure its limit, extending work of Bolley–Guillin–Villani (2007).

We study the relations between boundaries for algebras of holomorphic functions on Banach spaces and complex convexity of their balls. In addition, we show that the Shilov boundary for algebras of holomorphic functions on an order continuous sequence space X is the unit sphere SX if X is locally c-convex. In particular, it is shown that the unit sphere of the OrliczLorentz sequence space λφ,w i...