stability of solutions of symmetric stochastic differential equations with discontinuous driving semimartingales
Sample path average optimality of Markov control processes with strictly unbounded cost
We study the existence of sample path average cost (SPAC-) optimal policies for Markov control processes on Borel spaces with strictly unbounded costs, i.e., costs that grow without bound on the complement of compact subsets. Assuming only that the cost function is lower semicontinuous and that the transition law is weakly continuous, we show the existence of a relaxed policy with 'minimal' expected average cost and that the optimal average cost is the limit of discounted programs. Moreover, we...
Sample-path average cost optimality for semi-Markov control processes on Borel spaces: unbounded costs and mean holding times
We deal with semi-Markov control processes (SMCPs) on Borel spaces with unbounded cost and mean holding time. Under suitable growth conditions on the cost function and the mean holding time, together with stability properties of the embedded Markov chains, we show the equivalence of several average cost criteria as well as the existence of stationary optimal policies with respect to each of these criteria.
Sard's approximation processes and oblique projections
Three problems arising in approximation theory are studied. These problems have already been studied by Arthur Sard. The main goal of this paper is to use geometrical compatibility theory to extend Sard's results and get characterizations of the sets of solutions.
Seasonal time series with missing observations
Popular exponential smoothing methods dealt originally only with equally spaced observations. When time series contains gaps, smoothing constants have to be adjusted. Cipra et al., following Wright’s approach of irregularly spaced observations, have suggested ad hoc modification of smoothing constants for the Holt-Winters smoothing method. In this article the fact that the underlying model of the Holt-Winters method is a certain seasonal ARIMA is used. Minimum mean square error smoothing constants...
Second Order optimality in Markov decision chains
The article is devoted to Markov reward chains in discrete-time setting with finite state spaces. Unfortunately, the usual optimization criteria examined in the literature on Markov decision chains, such as a total discounted, total reward up to reaching some specific state (called the first passage models) or mean (average) reward optimality, may be quite insufficient to characterize the problem from the point of a decision maker. To this end it seems that it may be preferable if not necessary...
Selected multicriteria shortest path problems: an analysis of complexity, models and adaptation of standard algorithms
The paper presents selected multicriteria (multiobjective) approaches to shortest path problems. A classification of multi-objective shortest path (MOSP) problems is given. Different models of MOSP problems are discussed in detail. Methods of solving the formulated optimization problems are presented. An analysis of the complexity of the presented methods and ways of adapting of classical algorithms for solving multiobjective shortest path problems are described. A comparison of the effectiveness...
Selection theorems for stochastic set-valued integrals
Some special selections theorems for stochastic set-valued integrals with respect to the Lebesgue measure are given.
Self-tuning controls of linear stochastic systems in presence of drift
Selftuning LQ controllers with prespecified state
Self-tuning random early detection algorithm to improve performance of network transmission.
Self-tuning regulators with restricted inputs
Semi-group methods in stochastic control
Semi-Markov control models with average costs
This paper studies semi-Markov control models with Borel state and control spaces, and unbounded cost functions, under the average cost criterion. Conditions are given for (i) the existence of a solution to the average cost optimality equation, and for (ii) the existence of strong optimal control policies. These conditions are illustrated with a semi-Markov replacement model.
Sensor network design for the estimation of spatially distributed processes
In a typical moving contaminating source identification problem, after some type of biological or chemical contamination has occurred, there is a developing cloud of dangerous or toxic material. In order to detect and localize the contamination source, a sensor network can be used. Up to now, however, approaches aiming at guaranteeing a dense region coverage or satisfactory network connectivity have dominated this line of research and abstracted away from the mathematical description of the physical...
Sensor network scheduling for identification of spatially distributed processes
The work treats the problem of fault detection for processes described by partial differential equations as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A simple node activation strategy is discussed for the design of a sensor network deployed in a spatial domain that is supposed to be used while detecting changes in the underlying parameters which govern the process evolution. The setting considered relates to a...
Separation principle in the fractional Gaussian linear-quadratic regulator problem with partial observation
In this paper we solve the basic fractional analogue of the classical linear-quadratic Gaussian regulator problem in continuous-time with partial observation. For a controlled linear system where both the state and observation processes are driven by fractional Brownian motions, we describe explicitly the optimal control policy which minimizes a quadratic performance criterion. Actually, we show that a separation principle holds, i.e., the optimal control separates into two stages based on optimal...
Sequential identification algorithm and controller choice for a certain class of distributed systems
Set-valued and fuzzy stochastic integral equations driven by semimartingales under Osgood condition
We analyze the set-valued stochastic integral equations driven by continuous semimartingales and prove the existence and uniqueness of solutions to such equations in the framework of the hyperspace of nonempty, bounded, convex and closed subsets of the Hilbert space L2 (consisting of square integrable random vectors). The coefficients of the equations are assumed to satisfy the Osgood type condition that is a generalization of the Lipschitz condition. Continuous dependence of solutions with respect...
Set-valued stochastic integrals and stochastic inclusions in a plane
We present the concepts of set-valued stochastic integrals in a plane and prove the existence of a solution to stochastic integral inclusions of the form