Large deviations in the problem of distinguishing the counting processes

We prove the general limit theorem on probability of large deviations of the logarithm of the likelihood ratio with the null hypothesis and alternative. Weaker versions of the principle of large deviations are obtained in predictable terms for the problem of distinguishing the counting processes. The case of counting processes with deterministic compensators is studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 11, pp. 1514–1521, November, 1993.     

Convex Ordering for Random Vectors using Predictable Representation

We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and a non-necessarily independent jump component. Our method uses forward-backward stochastic calculus and extends the results proved in Klein et al. (Electron J Probab 11(20):27, 2006) in the one-dimensional case. We also study a geometric interpretation of convex ordering for discrete measures in connection with the conditions set on the jump heights and intensities of the considered processes. The work described in this paper was partially supported by a grant from City University of Hong Kong (Project No. 7200108).     

Optional and predictable projections of set-valued measurable processes

Abstract. In this paper,the optional and predictable projections of set-valued measurable pro-cesses are studied. The existence and uniqueness of optional and predictable projections of set-valued measurable processes are proved under proper circumstances.     

Projections and regularity of abstract processes

In this note we shall prove the existence of optional and predictable projections of stochastic processes X taking values in a Banach space E. Furthermore, if the range of X is contained in a compact set and if X is cadlag (respectively caglad), then the optional (respectively predictable) projection possesses the same property. Finally, we shall prove that every E-valued martingale has a cadlag modification     

Approximation of stochastic equations driven by predictable processes

Summary A theory of stochastic differential equations driven by predictable processes in Stratonovich sense is developed. These driving processes include a large class of discontinuous semimartingales. The theory of stochastic differential equations driven by continuous semimartingales in Stratonovich sense is extended without involving Lebesgue-Stieltjes integrals as done by Meyer. Moreover, a change of variables formula without extra terms involving the jumps of the processes holds for this theory. Results on approximation of driving processes are preserved.Research partially supported by the Institute for Mathematics and its Applications at the University of Minnesota, Minneapolis, USA; by the AFOSR under contract #AFOSR-85-0315, the ARO under contract #DAAG 29-84-K-0082, and #DAAL 03-86-K-0171.     

Embedding and asymptotic expansions for martingales

The paper develops a way of embedding general martingales in continuous ones in such a way that the quadratic variation of the continuous martingale has conditional cumulants (given the original martingale) that are explicitly given in terms of optional and predictable variations of the original process. Bartlett identities for the conditional cumulants are also found. A main corollary to these results is the establishment of second (and in some cases higher) order asymptotic expansions for martingales.Research supported in part by National Science Foundation grant DMS 93-05601 and Army Research Office grant DAAH04-1-0105     

Generalization of an inequality of Birnbaum and Marshall,with applications to growth rates for submartingales

The well-known submartingale maximal inquality of Birnbaum and Marshall (1961) is generalized to provide upper tail inequalities for suprema of processes which are products of a submartingale by a nonincreasing nonnegative predictable process. The new inequalities are proved by applying an inequality of Lenglart (1977), and are then used to provide best-possible universal growth-rates for a general submartingale in terms of the predictable compensator of its positive part. Applications of these growth rates include strong asymptotic upper bounds on solutions to certain stochastic differential equations, and strong asymptotic lower bounds on Brownian-motion occupation-times.     

Application of Moore-Penrose inverse in deciding the minimal martingale measure

The Moore-Penrose inverse is an important tool in algebra.This paper shows that the MoorePenrose inverse is also an effcient technique in determining the minimal martingale measure if a security price follows a semi-martingale which satisfies some structure condition.We extend a result of Dzhaparidze and Spreij concerning the Moore-Penrose inverse to the case that the Moore-Penrose inverse of any matrix-valued predictable process is still predictable.Furthermore,we obtain an explicit formula of the minimal martingale measure by employing the Moore-Penrose inverse.Specifically,the minimal martingale measure in a generalized Black-Scholes model is found.     

Adapting to the Changing Environment: A Theoretical Comparison of Decision Making Proficiency of Lean and Mass Organization Systems

In this paper weexamine the adaptability of the Japanese style leanorganization system and the traditional American style mass organizationsystem under changing environments. From an organizational designperspective, key structural aspects of the two organizations are modeled ina problem solving context using computational methods. Organizational-levelperformance in terms of decision making accuracy and severity of errors ismeasured as an indicator of organizational adaptability under conditionswhere the task environment shifts between predictable to unpredictable orvise versa. Our study shows that both organizations have their respectiveadvantages under different task environments and that they adapt toenvironmental shifts in different forms. Specifically, when the timepressure is high the lean organization system's performance isvirtually identical to the mass organization system, even though the leanorganization systemÆs members are more proactive. When the timepressure is low, the mass organization system shows a much fasteradaptability when the environment shifts to a predictable one but it is alsomore vulnerable when the environment shifts to an unpredictable one. Incontrast, the lean organization systemÆs response to the changingenvironment is characterized by its slower adaptability. When theenvironment shifts to an unpredictable one, the lean organization systemshows a gradual improvement till reaching a high level. When the environmentshifts to a predictable one, however, the lean organization system shows agradual decrease of performance. Our study further shows that the leanorganization system, with its strong team decision making emphasis, can bemore successful in avoiding severe errors when compared with the massorganization system, even under a predictable task environment.     

A composite material based on recycled tires

The present study is devoted to the elaboration and investigation of a composite material based on mechanically grinded recycled tires and a polymer binder. The correlation between the content of the binder, some technological parameters, and material properties of the composite was clarified. The apparent density, the compressive stress at a 10% strain, the compressive elastic modulus in static and cyclic loadings, and the insulating properties (acoustic and thermal) were the parameters of special interest of the present investigation. It is found that a purposeful variation of material composition and some technological parameters leads to multifunctional composite materials with different and predictable mechanical and insulation properties. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 145–150, January–February, 2009.     

Stopping for two-dimensional stochastic processes

The aim of this paper is to introduce some techniques that can be used in the study of stochastic processes which have as parameter set the positive quadrant of the plane R²₊. We define stopping lines and derive an interesting property of measurability for them. The notion of predictability is developed, and we show the connection between predictable processes, fields associated with stopping lines, and predictable stopping lines. We also give a theorem of section for predictable sets. Extension to processes indexed by any partially ordered set with some regularity assumptions can be carried out quite easily with the same techniques.     

L~Φ可料控制鞅Hardy-Orlicz空间之间的鞅变换

以鞅变换为工具,刻画了L^Φ可料控制鞅的Hardy-Orlicz空间之间的相互关系,设Φ₁和Φ₂是两个Young函数,并在某种意义上Φ₂强于Φ1（具体定义见正文）,以构造性的方法证明了Hardy-Orlicz空间D_Φ1中的鞅恰好是Hardy-Orlicz空间D_Φ2中的鞅的鞅变换.所得的结果推广了已有文献中的相关结论.     

集值随机过程的投影

本文研究了集值可积变差随机过程的可选和可料对偶投影．当Ｂａｎａｃｈ空间Ｘ具有ＲＮＰ,其对偶空间Ｘ＊可分时,证明了Ｐｗｋｃ（Ｘ）值的可积变差过程存在唯一的可选和可料对偶投影．最后讨论了集值随机过程对偶投影的性质．     

Greedy sums of distinct squares

When a positive integer is expressed as a sum of squares, with each successive summand as large as possible, the summands decrease rapidly in size until the very end, where one may find two 's, or several 's. We find that the set of integers for which the summands are distinct does not have a natural density but that the counting function oscillates in a predictable way.

     

矩阵损失下一般Gauss-Markov模型线性预测的可容许性

本文研究了一般Gauss-Markov模型中线性可预测变量的线性预测的可容许性.在给出线性预测可容许性定义的基础上,通过构造一个特殊的常量矩阵D0,分别得到了齐次和非齐次线性预测类中可容许的充要条件.     

Exploring a Multicriteria Approach to Production Scheduling

A current problem in production scheduling is related to the multi-criteria nature of the task. No matter how effective a heuristic or algorithm is, there remains a need to use human judgement to find a balance between an organization's conflicting objectives, such as meeting due-dates and minimizing work-in-progress. The problem is that heuristics do not have convenient input parameters that relate to these organizational objectives. In this paper we introduce the concept of a ‘control mechanism’ that would allow the scheduler to direct the search for a schedule on the basis of preferences with respect to multiple performance criteria. The feasibility of such a system is dependent on there being a predictable relationship between the input parameters of the scheduling heuristic and the performance measures. We describe a prototype Visual Interactive implementation of the proposed system, present the results of some initial experimental work, which indicates that the method has some potential, and comment on potentially fruitful areas for further research.     

Motoo理论的推广

在本文中，我们证明了右过程的正则集与可料停时不交，从而把本尾理论从Hunt过程推广到更一般的右过程。     

正态分布下任意秩有限总体中的Minimax预测

对于任意秩有限总体,在二次损失下,有关文献已给出了线性可预测变量在齐次线性预测类中的唯一线性Minimax预测．本文在正态假设下,证明了这个线性Minimax预测也是线性可预测变量在一切预测类中的唯一Minimax预测．     

任意秩有限总体中无偏预测和估计的构造关系

研究了有限总体均值向量的无偏估计和线性可预测变量的无偏预测之间的关系,利用分块矩阵广义逆直接对加权风险函数进行分解,提出了一种由均值向量的无偏估计来构造无偏预测的新方法,并找到了它们之间的构造关系.特别地,线性可预测变量的最优线性无偏预测(BLUP)可由均值向量的最佳线性无偏估计(BLUE)惟一地表示(有关惟一性在几乎处处意义下理解).     

A note on chaotic and predictable representations for Itô–Markov additive processes

In this article, we provide predictable and chaotic representations for Itô–Markov additive processes X. Such a process is governed by a finite-state continuous time Markov chain J which allows one to modify the parameters of the Itô-jump process (in so-called regime switching manner). In addition, the transition of J triggers the jump of X distributed depending on the states of J just prior to the transition. This family of processes includes Markov modulated Itô–Lévy processes and Markov additive processes. The derived chaotic representation of a square-integrable random variable is given as a sum of stochastic integrals with respect to some explicitly constructed orthogonal martingales. We identify the predictable representation of a square-integrable martingale as a sum of stochastic integrals of predictable processes with respect to Brownian motion and power-jumps martingales related to all the jumps appearing in the model. This result generalizes the seminal result of Jacod–Yor and is of importance in financial mathematics. The derived representation then allows one to enlarge the incomplete market by a series of power-jump assets and to price all market-derivatives.