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A class of stationary stochastic processes

Victor D. Didenko, Natalia A. Rozhenko (2014)

Studia Mathematica

Regular stationary stochastic vector processes whose spectral densities are the boundary values of matrix functions with bounded Nevanlinna characteristic are considered. A criterion for the representability of such processes as output data of linear time invariant dynamical systems is established.

A finite-buffer queue with a single vacation policy: an analytical study with evolutionary positioning

Marcin Woźniak, Wojciech M. Kempa, Marcin Gabryel, Robert K. Nowicki (2014)

International Journal of Applied Mathematics and Computer Science

In this paper, application of an evolutionary strategy to positioning a GI/M/1/N-type finite-buffer queueing system with exhaustive service and a single vacation policy is presented. The examined object is modeled by a conditional joint transform of the first busy period, the first idle time and the number of packets completely served during the first busy period. A mathematical model is defined recursively by means of input distributions. In the paper, an analytical study and numerical experiments...

A fuzzy approach to option pricing in a Levy process setting

Piotr Nowak, Maciej Romaniuk (2013)

International Journal of Applied Mathematics and Computer Science

In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets. We assume that some parameters of the financial instrument cannot be precisely described and therefore they are...

A mathematical framework for learning and adaption: (generalized) random systems with complete connections.

Ulrich Herkenrath, Radu Theodorescu (1981)

Trabajos de Estadística e Investigación Operativa

The aim of this paper is to show that the theory of (generalized) random systems with complete connection may serve as a mathematical framework for learning and adaption. Chapter 1 is of an introductory nature and gives a general description of the problems with which one is faced. In Chapter 2 the mathematical model and some results about it are explained. Chapter 3 deals with special learning and adaption models.

A probabilistic method for certification of analytically redundant systems

Bin Hu, Peter Seiler (2015)

International Journal of Applied Mathematics and Computer Science

Analytical fault detection algorithms have the potential to reduce the size, power and weight of safety-critical aerospace systems. Analytical redundancy has been successfully applied in many non-safety critical applications. However, acceptance for aerospace applications will require new methods to rigorously certify the impact of such algorithms on the overall system reliability. This paper presents a theoretical method to assess the probabilistic performance for an analytically redundant system....

A relaxation theorem for partially observed stochastic control on Hilbert space

N.U. Ahmed (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we present a result on relaxability of partially observed control problems for infinite dimensional stochastic systems in a Hilbert space. This is motivated by the fact that measure valued controls, also known as relaxed controls, are difficult to construct practically and so one must inquire if it is possible to approximate the solutions corresponding to measure valued controls by those corresponding to ordinary controls. Our main result is the relaxation theorem which states that...

Application of triple correlation and bispectrum for interference immunity improvement in telecommunications systems

Pavel Molchanov, Alexandr Totsky (2008)

International Journal of Applied Mathematics and Computer Science

This paper presents a new noise immunity encoding/decoding technique by using the features of triple correlation and bispectrum widely employed in digital signal processing systems operating in noise environments. The triple correlationand bispectrum-based encoding/decoding algorithm is tested for a digital radio telecommunications binary frequency shift keying system. The errorless decoding probability was analyzed by means of computer simulation for the transmission and reception of a test message...

Asymptotic stability condition for stochastic Markovian systems of differential equations

Efraim Shmerling (2010)

Mathematica Bohemica

Asymptotic stability of the zero solution for stochastic jump parameter systems of differential equations given by d X ( t ) = A ( ξ ( t ) ) X ( t ) d t + H ( ξ ( t ) ) X ( t ) d w ( t ) , where ξ ( t ) is a finite-valued Markov process and w(t) is a standard Wiener process, is considered. It is proved that the existence of a unique positive solution of the system of coupled Lyapunov matrix equations derived in the paper is a necessary asymptotic stability condition.

Attainability analysis in the problem of stochastic equilibria synthesis for nonlinear discrete systems

Irina Bashkirtseva, Lev Ryashko (2013)

International Journal of Applied Mathematics and Computer Science

A nonlinear discrete-time control system forced by stochastic disturbances is considered. We study the problem of synthesis of the regulator which stabilizes an equilibrium of the deterministic system and provides required scattering of random states near this equilibrium for the corresponding stochastic system. Our approach is based on the stochastic sensitivity functions technique. The necessary and important part of the examined control problem is an analysis of attainability. For 2D systems,...

Canonical input-output representation of linear multivariable stochastic systems and joint optimal parameter and state estimation.

G. Salut, J. Aguilar-Martín, S. Lefevre (1979)


In this paper a complete presentation is given of a new canonical representation of multi-input, multi-output linear stochastic systems. Its equivalence with operator form directly linked with ARMA processes as well as with classical state space representation is given, and a transfer matrix interpretation is developed in an example. The importance of the new representation is mainly in the fact that in the joint state and parameters estimation problem, all unknown parameters appear linearly when...

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