Usage of processes with continuous time in the study of stochastic recurrent sequences

The paper proposes a new approach connected with consideration of stochastic difference sequences like sequences of observations (in deterministic or random moments of time) of a continuous time process satisfying a stochastic differential equation.     

Imbedded construction of stationary sequences and point processes with a random memory

We show convergence in variation to a unique stationary state for a class of point processes (respectively, stochastic sequences) with stochastic intensity kernels (respectively, transition probabilities) including the (A,m)-processes of Lindvall [12]. This is done under two basic conditions: first, the random memory of the processes considered is consistent or non-reusable (that is, past information not used at a given time cannot be recalled at a later time) and secondly, the kernels have a deterministic fixed component for which the memory is almost surely finite.     

Bounds in Multistage Linear Stochastic Programming

Multistage stochastic programs, which involve sequences of decisions over time, are usually hard to solve in realistically sized problems. Providing bounds for optimal solution may help in evaluating whether it is worth the additional computations for the stochastic program vs. simplified approaches. In this paper we generalize measures from the two-stage case, based on different levels of available information, to the multistage stochastic programming problems. A set of theorems providing chains of inequalities among the new quantities are proved. Numerical results on a case study related to a simple transportation problem illustrate the described relationships.     

任意随机变量序列级数的强收敛性

利用鞅差序列级数的收敛定理和条件三级数定理研究了任意随机变量序列级数的强收敛性,推广了某些经典的鞅差序列和独立随机变量序列及两两NQD序列的强极限定理.     

Stochastic integral with respect to a semi-Markov process of diffusion type

We consider a multidimensional semi-Markov process of diffusion type. A stochastic integral with respect to the semi-Markov process is defined in terms of asymptotics related to the first exit time from a small neighborhood of the starting point of the process, and, in particular, in terms of its characteristic operator. This integral is equal to the sum of two other integrals: the first one is a curvilinear integral with respect to an additive functional defined in terms of the expected first exit time from a small neighborhood, and the second one is a stochastic integral with respect to a martingale of special kind. To prove the existence and to derive the properties of the integral, both the method of deducing sequences and that of inscribed ellipsoids are used. For Markov processes of diffusion type, the new definition of the stochastic integral is reduced to the standard one. Bibliography: 8 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 328, 2005, pp. 251–276.     

Stochastic cyclic flow lines: non-blocking,Markovian models

In this paper we consider stochastic cyclic flow lines where identical sets of jobs are repeatedly produced in the same loading and processing sequence. Each machine has an input buffer with enough capacity. Processing times are stochastic. We model the shop as a stochastic event graph, a class of Petri nets. We characterise the ergodicity condition and the cycle time. For the case where processing times are exponentially distributed, we present a way of computing queue length distributions. For two-machine cases, by the matrix geometric method, we compute the exact queue length distributions. For general cases, we present two methods for approximately decomposing the line model into two-machine submodels, one based on starvation propagation and the other based on transition enabling probability propagation. We experiment our approximate methods for various stochastic cyclic flow lines and discuss performance characteristics as well as accuracy of the approximate methods. Finally, we discuss the effects of job processing sequences of stochastic cyclic flow lines.     

Optimal Sequencing of Servers in the Two-Station Series Queueing System

This paper deals with determining an optimal sequence of service stations in a series queueing system. Optimality is defined in terms of the total time spent waiting for service. Sequences are compared on the basis of the moments of their steady-state total waiting time. In addition, the rules of stochastic dominance are applied which allow comparison of sequences on the basis of their waiting time distributions. Analytical results in the sequencing of service stations in series queues have been limited to stations with constant or exponential service times. This study extends the investigation to service distributions with varying degrees of statistical regularity given by the family of Erlang distributions.Relationships are developed for predicting optimal sequences. Validation is accomplished by simulating a number of systems and comparing the waiting time distribution functions for each sequence. The relationships are shown to be good predictors and useful in the study and design of systems of servers in series.     

Penalty method for solving a class of stochastic differential variational inequalities with an application

The aim of this paper is to study the penalty method for solving a class of stochastic differential variational inequalities (SDVIs). The penalty problem for solving SDVIs is first constructed and the convergence of the sequences generated by the penalty problem is proved under some mild conditions. As an application, the convergence of the sequences generated by the penalty problem is obtained for solving a stochastic migration equilibrium problem with movement cost.     

Detectability conditions for output-only subspace identification

ABSTRACT

The scope of output-only/blind identification is restricted to stochastic/statistical processes, but for the first time in this study, the detectability conditions for general output-only subspace identification are investigated. This aids the range of input sources to be extended in a much realistic manner, beyond the only stochastic inputs. For this purpose, the subspace framework is assigned to make a connection between the output signal contents and the LTI system order. A few substantial hypotheses and algebraic statements are propounded affirming the sufficiency of the genuine output sequences for the identification purpose. This can be perceived as the cornerstone of state-space model reconstruction. In order to consolidate the notions according to reality, several examples are studied and examined for different input classes with stochastic disturbance.     

Minimizing the expected weighted number of tardy jobs in stochastic flow shops

This paper is devoted to two types of stochastic scheduling problems, one involving a single machine and the other involving a flow shop consisting of an arbitrary number of machines. In both problem types, all jobs to be processed have due dates, and the objective is to find a job sequence that minimizes the expected weighted number of tardy jobs. For the single-machine case, sufficient optimality conditions for job sequences are derived for various choices of due date and processing time distributions. For the case of a flow shop with an arbitrary number of machines and identically distributed due dates for all jobs, we prove the following intuitively appealing results: (i) when all jobs have the same processing time distributions, the expected weighted number of tardy jobs is minimized by sequencing the jobs in decreasing order of the weights, (ii) when all weights are equal, the jobs should be sequenced according to an increasing stochastic ordering of the processing time distributions.     

任意随机组列的强极限定理

本文研究了任意随机组列的极限性质.利用构造鞅的方法得到了任意随机组列的强极限定理,所得结果摊广了任意随机适应序列和树上非齐次马氏链的强极限定理.     

On Weak Solutions of Stochastic Differential Equations

A new proof of existence of weak solutions to stochastic differential equations with continuous coefficients based on ideas from infinite-dimensional stochastic analysis is presented. The proof is fairly elementary, in particular, neither theorems on representation of martingales by stochastic integrals nor results on almost sure representation for tight sequences of random variables are needed.     

Identification of Stochastically Perturbed Autonomous Systems from Temporal Sequences of Probability Density Functions

The paper introduces a method for reconstructing one-dimensional iterated maps that are driven by an external control input and subjected to an additive stochastic perturbation, from sequences of probability density functions that are generated by the stochastic dynamical systems and observed experimentally.     

任意随机序列级数的强收敛性

利用鞅差序列级数收敛定理研究任意随机序列级数的强收敛性,得到了该序列的一个强极限定理,某些经典的鞅差序列和独立随机变量序列的强极限定理是其特例.     

Approximations for chance-constrained programming problems

This paper proposes an approximation approach to the solution of chance-constrained stochastic programming problems. The results rely in a fundamental way on the theory of convergence of sequences of measurable multifunctions. Particular results are presented for stochastic linear programming problems.     

Worst portfolios for dynamic monetary utility processes

We study the worst portfolios for a class of law invariant dynamic monetary utility functions with domain in a class of stochastic processes. The concept of comonotonicity is introduced for these processes in order to prove the existence of worst portfolios. Using robust representations of monetary utility function processes in discrete time, a relation between the worst portfolios at different periods of time is presented. Finally, we study conditions to achieve the maximum in the representation theorems for concave monetary utility functions that are continuous for bounded decreasing sequences.     

Characterization,parity, and power sequences of locally finite doubly stochastic matrices

We show that infinite locally finite doubly stochastic matrices are particular limits of sequences of finite doubly stochastic matrices and reciprocally. Thereby, we define the parity in the set of infinite locally finite doubly stochastic matrices. In particular, convexity and stability properties of the even matrix of this set are investigated, as well as the differences between the finite case and the infinite case. Moreover, the limits of the powers of locally finite infinite doubly stochastic matrices in this context are determined.     

A Series Approach to Stochastic Differential Equations with Infinite Dimensional Noise

This paper considers semilinear stochastic differential equations in Hilbert spaces with Lipschitz nonlinearities and with the noise terms driven by sequences of independent scalar Wiener processes (Brownian motions). The interpretation of such equations requires a stochastic integral. By means of a series of Itô integrals, an elementary and direct construction of a Hilbert space valued stochastic integral with respect to a sequence of independent scalar Wiener processes is given. As an application, existence and strong and weak uniqueness for the stochastic differential equation are shown by exploiting the series construction of the integral.     

关于机器随机故障完工时间方差最小化单机调度问题

讨论了机器随机故障时,工件完工时间方差的期望最小化单机调度问题,其中描述机器故障的计数过程为广义泊松过程.推导出了目标函数等价的确定形式,而后进一步给出了工件加工时间相同时问题的最优解.     

Weak solutions to stochastic 3D Navier-Stokes-α model of turbulence: α-Asymptotic behavior

We study the asymptotic behavior of weak solutions to the stochastic 3D Navier-Stokes-α model as α approaches zero. The main result provides a new construction of the weak solutions of stochastic 3D Navier-Stokes equations as approximations by sequences of solutions of the stochastic 3D Navier-Stokes-α model.