Estimating the efficient price from the order flow: A Brownian Cox process approach

At the ultra high frequency level, the notion of price of an asset is very ambiguous. Indeed, many different prices can be defined (last traded price, best bid price, mid price, etc.). Thus, in practice, market participants face the problem of choosing a price when implementing their strategies. In this work, we propose a notion of efficient price which seems relevant in practice. Furthermore, we provide a statistical methodology enabling to estimate this price from the order flow.     

Spaces with Dual Order-Isomorphic to ℓ1

We establish that an ordered Banach space is order-isomorphic to c₀ if and only if it is a -Dedekind complete vector lattice and its norm dual is order-isomorphic to ₁.     

Optimality for set functions with values in ordered vector spaces

Let (X, , ) be a finite atomless measure space,L a convex subfamily of , andY andZ locally convex Hausdorff topological vector spaces which are ordered by the conesC andD, respectively. LetF:LY beC-convex andG:LZ beD-convex set functions. Consider the following optimization problem (P): minimizeF(), subject to L andG() _D . The paper generalizes the Moreau-Rockafellar theorem with set functions. By applying this theorem, a Kuhn-Tucker type optimality condition and a Fritz John type optimality condition for problem (P) are established. The duality theorem for problem (P) is also studied.This work was partially supported by National Science Council, Taipei, Taiwan. This paper was written while the first author was visiting at the University of Iowa, 1987-88.The authors would like to express their gratitude to the two anonymous referees for their valuable comments. Also, they would like to thank Professor P. L. Yu for his encouragement and suggestions which improved the material presented here considerably.     

The multisublinear maximal type operators in Banach function lattices

The main aim of this paper is to study a general multisublinear operators generated by quasi-concave functions between weighted Banach function lattices. These operators, in particular, generalize the Hardy–Littlewood and fractional maximal functions playing an important role in harmonic analysis. We prove that under some general geometrical assumptions on Banach function lattices two-weight weak type and also strong type estimates for these operators are true. To derive the main results of this paper we characterize the strong type estimate for a variant of multilinear averaging operators. As special cases we provide boundedness results for fractional maximal operators in concrete function spaces.     

Parametric and Non Homogeneous Semi-Markov Process for HIV Control

In AIDS control, physicians have a growing need to use pragmatically useful and interpretable tools in their daily medical taking care of patients. Semi-Markov process seems to be well adapted to model the evolution of HIV-1 infected patients. In this study, we introduce and define a non homogeneous semi-Markov (NHSM) model in continuous time. Then the problem of finding the equations that describe the biological evolution of patient is studied and the interval transition probabilities are computed. A parametric approach is used and the maximum likelihood estimators of the process are given. A Monte Carlo algorithm is presented for realizing non homogeneous semi-Markov trajectories. As results, interval transition probabilities are computed for distinct times and follow-up has an impact on the evolution of patients.      

Geometry effect on the magnetic ordering of geometrically frustrated rectangular and triangular magnets

We investigate the effect of geometry on the ground-state ordering of artificially frustrated magnetic rectangular and triangular lattices by Monte Carlo method. By varying the vertical lattice spacing while keeping the horizontal one fixed, we show that when the ratio of vertical to horizontal lattice spacing, labeled by η, is less than 1.82, the ground state of the rectangular lattice presents long-range antiferromagnetic order and for η?1.82 the ground state changes to long-range mixed ferromagnetic and antiferromagnetic order. For the frustrated triangular lattice, the short-range ordered state as well as two long-range ordered ground states occurs transiently at η=0.87 and 2, where the energies of the two ground states with long-range order are approximately equal. In addition, the level of frustration of both frustrated lattices is found to be largely relevant to the ratio η.     

Lattice Attacks on Digital Signature Schemes

We describe a lattice attack on the Digital Signature Algorithm (DSA) when used to sign many messages, m_i, under the assumption that a proportion of the bits of each of the associated ephemeral keys, y_i, can be recovered by alternative techniques.     

不精确数据的相似度及其在聚类分析中的应用

基本包含度理论,提出不精确数据的一种相似度,并讨论基于此相似度的不精确数据的聚类方法。     

On Banach spaces with Kasparov and Yu's Property (H)

A new geometric property of Banach spaces recently introduced by G. Kasparov and G. Yu, called Property (H), has important applications to the strong Novikov conjecture and the coarse Novikov conjecture, yet is far from being well understood. In this paper, we investigate various uniformly continuous maps on unit spheres of Banach spaces and prove that all separable Banach lattices with nontrivial cotype have Property (H).     

Characterization of semi-classical orthogonal polynomials on nonuniform lattices

We state and prove characterization theorem for semi-classical orthogonal polynomials on nonuniform lattices (quadratic lattices of a discrete or q-discrete variable). This theorem proves the equivalence between the four characterization properties, namely, the Pearson type equation for the linear functional, the strictly quasi-orthogonality of the derivatives, the structure relation, and the Riccati equation for the formal Stieltjes function. We give the classification of the semi-classical linear functional of class one on nonuniform lattice. Using the definition and the properties of the associated orthogonal polynomials, we prove that semi-classical orthogonal polynomials satisfy the second-order divided difference equation on nonuniform lattices.