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 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 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

scholarly journals Model of Stabilizing of the Interest Rate on Deposits Banking System Using by Moment Equations

2013 ◽  
Vol 54 (1) ◽  
pp. 45-59 ◽  
Author(s):  
Irada Dzhalladova ◽  
Mária Michalková ◽  
Miroslava Růžičková
Keyword(s):  
Interest Rate ◽  
Markov Chains ◽  
Difference Equations ◽  
Functional Equations ◽  
Banking System ◽  
Moment Equations ◽  
System Of Difference Equations ◽  
Economic Problems ◽  
The Interest Rate ◽  
The Moment

Abstract The paper deals with a system of difference equations, where coefficients depend on Markov chains. The functional equations for particular density and the moment equations for the system are derived and used in the investigation of solvability and stability. An application of the results is shown how to solve various economic problems.

scholarly journals Dynamic system with random structure for modeling security and risk management in cyberspace

2019 ◽  
Vol 39 (1) ◽  
pp. 23-37 ◽  
Author(s):  
Irada Dzhalladova ◽  
Miroslava Růžičková
Keyword(s):  
Risk Management ◽  
Markov Chain ◽  
Dynamic System ◽  
Difference Equations ◽  
Trivial Solution ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Random Structure ◽  
System Of Difference Equations ◽  
Necessary And Sufficient

We deal with the investigation of \(L_{2}\)-stability of the trivial solution to the system of difference equations with coefficients depending on a semi-Markov chain. In our considerations, random transformations of solutions are assumed. Necessary and sufficient conditions for \(L_{2}\)-stability of the trivial solution to such systems are obtained. A method is proposed for constructing Lyapunov functions and the conditions for its existence are justified. The dynamic system and methods discussed in the paper are very well suited for use as models for protecting information in cyberspace.

scholarly journals TRANSAKSI VALUTA ASING (AL-SHARF) DALAM PERSPEKTIF ISLAM

IQTISHODUNA ◽  
2011 ◽  
Vol 3 (2) ◽  
Author(s):  
Muhammad Sulhan
Keyword(s):  
International Trade ◽  
Foreign Exchange ◽  
Foreign Exchange Market ◽  
Foreign Currency ◽  
Islamic Law ◽  
Exchange Market ◽  
Demand And Supply ◽  
Written Text ◽  
The Moment ◽  
Currency Conversion

The written text attempts to explain transactional problem (trade) foreign exchange of Islamic law trade. It is caused by the international trade phenomena that won’t be free from state currency one another as a payment tool in which accelerate the traffic of international trade activity.  The necessity of currency conversion in the international trade will bring up out of foreign exchange demand and supply in the foreign exchange market; it will cause foreign exchange trade transaction at last. Based on the variety of Islamic laws analysis, it is known that the foreign currency  trade practice (al-sharf) is allowed if done based on each other agreement and cash, not to have a speculation (undertake something hoping for the best), there is transactional needed or aware of (saving), and if the transaction done toward the same type of currency so, it must have the same value and if it’s different, it must be done using prevailed rate of exchange (kurs)  in the moment of transaction. The following types of foreign exchange transaction in the foreign exchange market, it is only spot transactional type allowed, meanwhile forward, swap, and option are forbidden because they aren’t cash and contain of maisir (speculation). Besides, the participants should pay more attention toward constrains of foreign exchange trade transaction and they should be able to avoid divergences that are forbidden in Islamic of syariah trade like extortionate, forcing and many others. In this case, these cause the transaction of foreign exchange trade is prohibited.

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