关于双重时序AR-MA模型的相关结构及与ARMA模型的比较

本文在文［４］的基础上讨论了双重时序ＡＲ（１）－ＭＡ（ｑ）模型的相关结构，在不假定白噪声序列为正态的情况下，证明了安鸿志［２］关于模型的相关结构的猜想是正确的，具体地构造了ＡＲ（１）－ＭＡ（３）模型的相关结构，并与ＡＲＭＡ模型进行了初步的比较，给出了一些抛砖引玉的讨论．     

Contingent epiderivatives and set-valued optimization

In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional derivatives in the single-valued convex case. For optimization problems with a set-valued objective function optimality conditions based on the concept of the contingent epiderivative are proved which are necessary and sufficient under suitable assumptions.     

Soluble models for dynamics driven by a super-diffusive noise

We explicitly discuss scalar Langevin type of equations where the deterministic part is linear, but where the integrated noise source is a non-linear diffusion process exhibiting superdiffusive behavior. We calculate transient and stationary probabilities and study the possibility of noise induced transitions from a unimodal to a bimodal probability shape. Illustrations from finance and dynamical systems are given.     

SPAR: stochastic programming with adversarial recourse

We consider a general adversarial stochastic optimization model. Our model involves the design of a system that an adversary may subsequently attempt to destroy or degrade. We introduce SPAR, which utilizes mixed-integer programming for the design decision and a Markov decision process (MDP) for the modeling of our adversarial phase.     

Theoretical and computational studies of vectorial processes in biomolecular systems

Efficient vectorial processes such as the transduction of bioenergy and signals are characteristics that strikingly distinguish living systems from inanimate materials. Recent developments in biophysical and biochemical techniques have provided new information about the structure, dynamics and interaction of biomolecules involved in vectorial life processes at multiple length and temporal scales. This wealth of data makes it possible to carry out theoretical and computational studied of key mechanistic questions associated with complex life processes at an unprecedented level. Using two “vectorial biomolecular machines”, myosin and cytochrome c oxidase, as examples, we discuss the identification of interesting and biologically relevant questions that require thorough theoretical analysis. Technical challenges and recent progress related to these theoretical investigations are briefly summarized     

Large deviation principle for enhanced Gaussian processes

We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölder- or modulus topology, appears as special case.     

Effect of a thermal radiation field on the γ-luminescence of alkali-silicate glass

We revealed the changes in the γ-luminescence spectra under the influence of a thermal radiation field on high-purity alkali-silicate glasses (I) and those with addition of Fe³⁺ ions (II). We explain the obtained results within the framework of the L-model of edge absorption and electron-hole recombination processes. Samarkand State University, 15, Universitetskii Bul., Samarkand, 703004, Republic of Uzbekistan. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 3, pp. 453–455, May–June, 1998.     

Symmetric form of the Hudson-Parthasarathy stochastic equation

We prove that the Hudson-Parthasarathy equation corresponds, up to unitary equivalence, to the strong resolvent limit of Schrödinger Hamiltonians in Fock space and that the symmetric form of this equation corresponds to the weak limit of the Schrödinger Hamiltonians.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 726–750, November, 1996.     

Proof of the Mixing Theorem for Statistical Systems in Classical Physics

In a general measure-theoretic context, it is proved that the action of a stochastic map on a pair of probability distributions can be characterized by the criterion of decreasing mixing distance.     

Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions

Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes.