scholarly journals Moment Equations in Modeling a Stable Foreign Currency Exchange Market in Conditions of Uncertainty

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Josef Diblík ◽  
Irada Dzhalladova ◽  
Mária Michalková ◽  
Miroslava Růžičková
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Markov Process ◽  
Linear Differential Equation ◽  
Foreign Currency ◽  
Exchange Market ◽  
Moment Equations ◽  
Currency Exchange ◽  
Semi Markov Process ◽  
Linear Differential

The paper develops a mathematical model of foreign currency exchange market in the form of a stochastic linear differential equation with coefficients depending on a semi-Markov process. The boundaries of the domain of its instability is determined by using moment equations.

scholarly journals A Dynamical System with Random Parameters as a Mathematical Model of Real Phenomena

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1338 ◽  
Author(s):  
Josef Diblík ◽  
Irada Dzhalladova ◽  
Miroslava Růžičková
Keyword(s):  
Markov Chain ◽  
Difference Equations ◽  
Foreign Currency ◽  
Random Structure ◽  
Exchange Market ◽  
Moment Equations ◽  
Random Parameters ◽  
Linear Difference Equations ◽  
Currency Exchange ◽  
The Moment

In many cases, it is difficult to find a solution to a system of difference equations with random structure in a closed form. Thus, a random process, which is the solution to such a system, can be described in another way, for example, by its moments. In this paper, we consider systems of linear difference equations whose coefficients depend on a random Markov or semi-Markov chain with jumps. The moment equations are derived for such a system when the random structure is determined by a Markov chain with jumps. As an example, three processes: Threats to security in cyberspace, radiocarbon dating, and stability of the foreign currency exchange market are modelled by systems of difference equations with random parameters that depend on a semi-Markov or Markov process. The moment equations are used to obtain the conditions under which the processes are stable.

scholarly journals Application of methods of system analysis for modeling the process of distance learning

2021 ◽  
pp. 64-67
Author(s):  
S. Ya. Zhukovich
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Distance Learning ◽  
Control Theory ◽  
Linear Differential Equation ◽  
System Analysis ◽  
Current Knowledge ◽  
Linear Differential ◽  
The Individual ◽  
Individual Trainee

A mathematical model of distance learning based on control theory in the form of an inhomogeneous linear differential equation is proposed. On the basis of the coefficients of assimilation and forgetting, determined with the help of special tests, it is possible to predict, in some approximation, the level of current knowledge of both the individual trainee and the group or stream of students.

Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kusano Takaŝi ◽  
Jelena V. Manojlović
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Continuous Function ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Regular Variation ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Positive Continuous Function ◽  
Linear Differential

AbstractWe study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation(p(t)\lvert x^{\prime}\rvert^{\alpha}\operatorname{sgn}x^{\prime})^{\prime}+q(% t)\lvert x\rvert^{\alpha}\operatorname{sgn}x=0,where q is a continuous function which may take both positive and negative values in any neighborhood of infinity and p is a positive continuous function satisfying one of the conditions\int_{a}^{\infty}\frac{ds}{p(s)^{1/\alpha}}=\infty\quad\text{or}\quad\int_{a}^% {\infty}\frac{ds}{p(s)^{1/\alpha}}<\infty.The asymptotic formulas for generalized regularly varying solutions are established using the Karamata theory of regular variation.

scholarly journals Steady Motion of Ice Sheets

1980 ◽  
Vol 25 (92) ◽  
pp. 229-246 ◽  
Author(s):  
L. W. Morland ◽  
I. R. Johnson
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Power Law ◽  
Perturbation Expansion ◽  
Ice Sheet ◽  
Leading Order ◽  
Plane Flow ◽  
General Law ◽  
Non Linear ◽  
Linear Differential

AbstractSteady plane flow under gravity of a symmetric ice sheet resting on a horizontal rigid bed, subject to surface accumulation and ablation, basal drainage, and basal sliding according to a shear-traction-velocity power law, is treated. The surface accumulation is taken to depend on height, and the drainage and sliding coefficient also depend on the height of overlying ice. The ice is described as a general non-linearly viscous incompressible fluid, with illustrations presented for Glen’s power law, the polynomial law of Colbeck and Evans, and a Newtonian fluid. Uniform temperature is assumed so that effects of a realistic temperature distribution on the ice response are not taken into account. In dimensionless variables a small paramter ν occurs, but the ν = 0 solution corresponds to an unbounded sheet of uniform depth. To obtain a bounded sheet, a horizontal coordinate scaling by a small factor ε(ν) is required, so that the aspect ratio ε of a steady ice sheet is determined by the ice properties, accumulation magnitude, and the magnitude of the central thickness. A perturbation expansion in ε gives simple leading-order terms for the stress and velocity components, and generates a first order non-linear differential equation for the free-surface slope, which is then integrated to determine the profile. The non-linear differential equation can be solved explicitly for a linear sliding law in the Newtonian case. For the general law it is shown that the leading-order approximation is valid both at the margin and in the central zone provided that the power and coefficient in the sliding law satisfy certain restrictions.

A property of the asymptotic series for a class of Titchmarsh–Weyl m-functions

1986 ◽  
Vol 102 (3-4) ◽  
pp. 253-257 ◽  
Author(s):  
B. J. Harris
Keyword(s):  
Differential Equation ◽  
Asymptotic Expansion ◽  
Linear Differential Equation ◽  
Asymptotic Series ◽  
Second Order ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
The Real ◽  
Linear Differential ◽  
Image Position

SynopsisIn an earlier paper [6] we showed that if q ϵ CN[0, ε) for some ε > 0, then the Titchmarsh–Weyl m(λ) function associated with the second order linear differential equationhas the asymptotic expansionas |A| →∞ in a sector of the form 0 < δ < arg λ < π – δ.We show that if the real valued function q admits the expansionin a neighbourhood of 0, then

scholarly journals Analysis of a network structure of the foreign currency exchange market

2009 ◽  
Vol 4 (1) ◽  
pp. 55-72 ◽  
Author(s):  
Jarosław Kwapień ◽  
Sylwia Gworek ◽  
Stanisław Drożdż ◽  
Andrzej Górski
Keyword(s):  
Network Structure ◽  
Foreign Currency ◽  
Exchange Market ◽  
Currency Exchange
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