We consider a sequence of Markov chains that weakly converge to a diffusion process. We assume that the trend contains a linearly growing component. The usual parametrix method does not apply since the trend is unbounded. We show how to modify the parametrix method in order to get local limit theorems in this case.

For the space transport systems with a long uptime, consideration was given to the method of adaptive filtering in the problem of restoring the parameters of cosmic radiation flows from the measurement data. Proposed were a mathematical model and an algorithm for optimization of the nonstationary control systems whose state is measured against the noisy background. The algorithms of parametric optimization were based on a modified Wiener–Hopf equation and sensitivity functions.

Consideration was given to the classical *NP*-hard problem 1|*r* *j* |*L* max of the scheduling theory. An algorithm to determine the optimal schedule of processing *n* jobs where the job parameters satisfy a system of linear constraints was presented. The polynomially solvable area of the problem 1|*r* *j* |*L* maxwas expanded. An algorithm was described to construct a Pareto-optimal set of schedules by the criteria *L* max and *C* max for complexity of *O*(*n* 3log*n*) operations.

We consider the planning problem for freight transportation between two railroad stations. We are required to fulfill orders (transport cars by trains) that arrive at arbitrary time moments and have different value (weight). The speed of trains moving between stations may be different. We consider problem settings with both fixed and undefined departure times for the trains. For the problem with fixed train departure times we propose an algorithm for minimizing the weighted lateness of orders with time complexity *O*(*qn*2 log *n*) operations, where *q* is the number of trains and *n* is the number of orders. For the problem with undefined train departure and arrival times we construct a Pareto optimal set of schedules optimal with respect to criteria *wL*max and *C*max in *O*(*n*2 max{*n* log *n*, *q* log *v*}) operations, where *v* is the number of time windows during which the trains can depart. The proposed algorithm allows to minimize both weighted lateness *wL*max and total time of fulfilling freight delivery orders *C*max.

This paper systematizes the empirical results on efficiency concepts applied to higher education institutions, data envelopment analysis (DEA) adjusted to heterogeneous samples, inputs and outputs chosen for these institutions and factors tended to make universities efficient. Special attention is paid to the consistency of results yielded by different models.

This paper considers a monopolistic competition model with the endogenous choice of technology in the closed economy case. Our aim is to obtain the comparative statics of the equilibrium and socially optimal solutions with respect to the technological innovation parameter that affects costs. The key findings are the following: consumption and investments in productivity both increase with the growth of technological innovation; the behavior of the equilibrium variables depends on the elasticity of demand only; the behavior of the socially optimal variables depends on the elasticity of utility only; finally, the behavior of the equilibrium and socially optimal variables does not depend on the properties of the costs as a function of investments in R&D.

Consideration was given to the omega square Cramer–von Mises tests intended to verify the goodness hypothesis about the distribution of the observed multivariable random vector with the distribution in the unit cube. The limit distribution of the statistics of these tests was defined by the distribution of an infinite quadratic form in the normal random variables. For convenience of computing its distribution, the residue of the quadratic form was approximated by a finite linear combination of the χ2-distributed random variables. Formulas for determination of the residue parameters were established.

We consider the diffusion process and its approximation by Markov chain with nonlinear unbounded trends. The usual parametrix method is not applicable because these models have unbounded trends. We describe a procedure that allows to exclude nonlinear unbounded trend and move to stochastic differential equation with bounded drift and diffusion coefficients. A similar procedure is considered for a Markov chain.

The application of the object-attribute (OA) architecture of computing environment to implementation of distributed automation systems with computational nodes (computers or PLCs) of different hardware architectures is described. The features of OA modeling of distributed automation tools and the main techniques for modeling, programming, and debugging of such systems are shown.

For a linear stochastic control system with quadratic objective functional, we introduce various generalizations of the notions of optimality on average and stochastic optimality on an infinite time interval that take into account possible degeneration of the parameter of the disturbing process with time (attenuation of the disturbances) or the presence of a discount function in the objective functional. This lets us improve upon the quality estimate for a well known optimal control in this problem from the point of view of both asymptotic behavior of the functional’s expectation and its asymptotic probabilistic properties. In particular, in the considered case we have found an improvement for the well known logarithmic upper bound on the optimal control for a family of defect processes.

We consider a control problem over an infinite time horizon with a linear stochastic system with an unstable asymptotically unbounded state matrix. We extend the notion of anti-stability of a matrix to the case of non-exponential anti-stability, and introduce an antistability rate function as a characteristic of the rate of growth for the norm of the corresponding fundamental matrix. We show that the linear stable feedback control law is optimal with respect to the criterion of the adjusted extended long-run average. The designed criterion explicitly includes information about the rate of anti-stability and the parameters of the disturbances. We also analyze optimality conditions.

Consideration was given to optimization of the queue control strategy in the MlGl1l queuing system where decision about continuing or stopping admission of customers is made at the service completion instants of each customer in compliance with the distribution on the set of decisions depending on the number of customers remaining in the system. The mean specific income in the stationary mode was used as the efficiency criterion and the set of permissible strategies coincided with the set of homogeneous randomised Markov strategies. It was proved that if there exists an optimal strategy, then it is degenerate and threshold with one point on control switching, that is, if the number of customers in the system exceeds a certain level, then admission of customers must be stooped or, otherwise, it must be continued.

We consider the problem of stochastic linear regulator over an infinite time horizon with superexponentially stable matrix in the equation of state dynamics. The form of the optimal control based on the criterion taking into account the information about the parameters of disturbances and the matrix stability rate was determined. The results obtained were used to analyze the model of a system with extremely impatient agents where the objective functional includes discounting by the asymptotically unbounded rate.

We find optimal (from the insurer’s point of view) strategies for insurance and reinsurance

in a controllable Cramer–Lundberg risk process that describes the capital dynamics of

an insurance company over an infinite time interval. As the optimality criterion being minimized,

we use the stationary variation coefficient, taking into account additional constraints

on residual risks for both insurers and reinsurer. We establish that it is best to use stop-loss

reinsurance with an upper limit and insurance which is a combination of a stop-loss strategy

and deductible. Equations that define optimal strategies parameters are derived.