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Kybernetes, vol. 41 no. 7/8
Type: Research Article
ISSN: 0368-492X

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Article

Edita Kolarova and Lubomir Brancik

The purpose of this paper is to determine confidence intervals for the stochastic solutions in RLCG cells with a potential source influenced by coloured noise.

Abstract

Purpose

The purpose of this paper is to determine confidence intervals for the stochastic solutions in RLCG cells with a potential source influenced by coloured noise.

Design/methodology/approach

The deterministic model of the basic RLCG cell leads to an ordinary differential equation. In this paper, a stochastic model is formulated and the corresponding stochastic differential equation is analysed using the Itô stochastic calculus.

Findings

Equations for the first and the second moment of the stochastic solution of the coloured noise-affected RLCG cell are obtained, and the corresponding confidence intervals are determined. The moment equations lead to ordinary differential equations, which are solved numerically by an implicit Euler scheme, which turns out to be very effective. For comparison, the confidence intervals are computed statistically by an implementation of the Euler scheme using stochastic differential equations.

Practical implications/implications

The theoretical results are illustrated by examples. Numerical simulations in the examples are carried out using Matlab. A possible generalization for transmission line models is indicated.

Originality/value

The Itô-type stochastic differential equation describing the coloured noise RLCG cell is formulated, and equations for the respective moments are derived. Owing to this original approach, the confidence intervals can be found more effectively by solving a system of ordinary differential equations rather than by using statistical methods.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 4
Type: Research Article
ISSN: 0332-1649

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Article

Shuang Xu and Ran Zhang

The purpose of this paper is to investigate how to determine optimal investing stopping time in a stochastic environment, such as with stochastic returns, stochastic

Abstract

Purpose

The purpose of this paper is to investigate how to determine optimal investing stopping time in a stochastic environment, such as with stochastic returns, stochastic interest rate and stochastic expected growth rate.

Design/methodology/approach

Transformation method was used for solving optimal stopping problem by providing a way to transform path‐dependent problem into a path‐independent one. Based on option pricing theory, optimal investing stopping time was thought of as an optimal executed timing problem of American‐style option.

Findings

First, the authors transform a path‐dependent stop timing problem to a path‐independent one with transformation under very general conditions, to directly use the existing conclusion of optimal stopping time literature. Second, when dynamics of capital growth is homogeneous, the authors changed the two dimensional optimal stop timing problem into a single dimension problem based on the assumption of zero exercise costs. Third, the authors investigated the comparative dynamics about asset selling boundary on asset value, state variable and return predictability. With constant discount rate and growth rate, the optimal selling timing depends on the simple comparison between capital cost and growth rate.

Originality/value

The paper's contributions to analysis method may be as follows. The authors demonstrate how to transform a path‐dependent stopping problem into a path‐independent one under general conditions. The transform method in this article can be applied to other path‐dependent optimal stopping problems. In particular, a Riccati ordinary differential equation for the transformation is set up. In most examples commonly met in finance, the equation can be solved explicitly.

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China Finance Review International, vol. 3 no. 2
Type: Research Article
ISSN: 2044-1398

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Article

Rahman Farnoosh, Parisa Nabati, Ramazan Rezaeyan and Morteza Ebrahimi

The purpose of this paper is to analyze the effect of the white, colored and mixture noise perturbations as Gaussian process on the parameters of the RL electrical circuit…

Abstract

Purpose

The purpose of this paper is to analyze the effect of the white, colored and mixture noise perturbations as Gaussian process on the parameters of the RL electrical circuit including potential source and resistance.

Design/methodology/approach

By adding different noise terms in the voltage and resistance parameters of an RL electrical circuit, the deterministic model is replaced by a stochastic differential equation (SDE).

Findings

Owing to the application of multiple Ito's formula the analytical solutions of resulted SDEs have been obtained. Furthermore, based on a numerical method involving Euler‐Maruyama scheme, the solution of the problem at the point of interest as a continuous time stochastic process has been obtained. Also shown is that the confidence interval for mean of solutions with colored and mixture noises is better than white noise.

Practical implications

Numerical tests via Matlab programming are performed in order to show the efficiency and accuracy of the present work. Numerical experiments show that an excellent estimation on the solution can be obtained within a couple of minutes time at Pentium IV‐2.4 GHz PC.

Originality/value

It is believed that the stochastic model of an RL circuit with colored and mixture noises in potential source has not been studied before. Furthermore, according to latest information from the research works, two stochastic parameters in voltage and resistance of RL circuit including colored and mixture noise processes have been investigated for the first time in this paper.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 2
Type: Research Article
ISSN: 0332-1649

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Article

G. ADOMIAN and R. RACH

The decomposition method of Adomian, which was developed to solve nonlinear stochastic differential equations, has recently been generalized in a number of directions and…

Abstract

The decomposition method of Adomian, which was developed to solve nonlinear stochastic differential equations, has recently been generalized in a number of directions and is now applicable to wide classes of linear and nonlinear, deterministic and stochastic differential, partial differential, and differential delay equations as well as algebraic equations of all types including polynomial equations, matrix equations, equations with negative or nonintegral powers, and random algebraic equations. This paper will demonstrate applicability to transcendental equations as well. The decomposition method basically considers operator equations of the form Fu = g where g may be a number, a function, or even a stochastic process. F is an operator which in general is nonlinear. (If it involves stochastic processes as well, we use a script letter F). The operator F may be a differential or algebraic operator. In this paper we will concentrate on the latter. The authors have thus developed a useful system for realistic solutions of real‐world problems.

Details

Kybernetes, vol. 15 no. 1
Type: Research Article
ISSN: 0368-492X

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Article

Marcin Kamiński and Graham F. Carey

To generalize the traditional 2nd order stochastic perturbation technique for input random variables and fields and to demonstrate for flow problems.

Abstract

Purpose

To generalize the traditional 2nd order stochastic perturbation technique for input random variables and fields and to demonstrate for flow problems.

Design/methodology/approach

The methodology is based on an n‐th order expansion (perturbation) for input random parameters and state functions around their expected value to recover probabilistic moments of the response. A finite element formulation permits stochastic simulations on irregular meshes for practical applications.

Findings

The methodology permits approximation of expected values and covariances of quantities such as the fluid pressure and flow velocity using both symbolic and discrete FEM computations. It is applied to inviscid irrotational flow, Poiseulle flow and viscous Couette flow with randomly perturbed boundary conditions, channel height and fluid viscosity to illustrate the scheme.

Research limitations/implications

The focus of the present work is on the basic concepts as a foundation for extension to engineering applications. The formulation for the viscous incompressible problem can be implemented by extending a 3D viscous primitive variable finite element code as outlined in the paper. For the case where the physical parameters are temperature dependent this will necessitate solution of highly non‐linear stochastic differential equations.

Practical implications

Techniques presented here provide an efficient approach for numerical analyses of heat transfer and fluid flow problems, where input design parameters and/or physical quantities may have small random fluctuations. Such an analysis provides a basis for stochastic computational reliability analysis.

Originality/value

The mathematical formulation and computational implementation of the generalized perturbation‐based stochastic finite element method (SFEM) is the main contribution of the paper.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 15 no. 7
Type: Research Article
ISSN: 0961-5539

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Article

Farshid Mirzaee and Nasrin Samadyar

The purpose of this paper is to develop a new method based on operational matrices of Bernoulli wavelet for solving linear stochastic Itô-Volterra integral equations, numerically.

Abstract

Purpose

The purpose of this paper is to develop a new method based on operational matrices of Bernoulli wavelet for solving linear stochastic Itô-Volterra integral equations, numerically.

Design/methodology/approach

For this aim, Bernoulli polynomials and Bernoulli wavelet are introduced, and their properties are expressed. Then, the operational matrix and the stochastic operational matrix of integration based on Bernoulli wavelet are calculated for the first time.

Findings

By applying these matrices, the main problem would be transformed into a linear system of algebraic equations which can be solved by using a suitable numerical method. Also, a few results related to error estimate and convergence analysis of the proposed scheme are investigated.

Originality/value

Two numerical examples are included to demonstrate the accuracy and efficiency of the proposed method. All of the numerical calculation is performed on a personal computer by running some codes written in MATLAB software.

Details

Multidiscipline Modeling in Materials and Structures, vol. 15 no. 3
Type: Research Article
ISSN: 1573-6105

Keywords

Abstract

Details

Optimal Growth Economics: An Investigation of the Contemporary Issues and the Prospect for Sustainable Growth
Type: Book
ISBN: 978-0-44450-860-7

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Article

Xiaojing Zheng, Xusong Xu and Cui Cui Luo

The purpose of this paper is to improve the behaviors coordination mechanism, to maintain the system's long time‐scale and stable competitive capability, when the agents…

Abstract

Purpose

The purpose of this paper is to improve the behaviors coordination mechanism, to maintain the system's long time‐scale and stable competitive capability, when the agents in the system focus on cooperating with each other.

Design/methodology/approach

Effort level for every agent, whose dynamics can be described as a stochastic partial differential equation, and the incentive of effort as the control of the corresponding agent, are introduced to describe agents' behavior abstracted. The cooperative stochastic differential game model is constructed: first, the optimal resolve trajectory mapping with profit maximization of the system are obtained, then the transitory imputation coupled with effort initial state of the system by introducing dynamic Shapley value imputation method. Based on the results obtained, the profit distribution strategies and the equilibration incentive compensation mechanism are given, due to the evolution law of the payoff and the state variable.

Findings

It is concluded that: the transitory compensation to agent for efforts and incentive, which can be changed with the system state at current and in history and in future changed, would guarantee the realization of the Shapley value imputation throughout the game horizon.

Originality/value

In this paper, the interactivity between agents in the system is considered first. The dynamical Shapley imputation mechanism and the transitory compensatory mechanism are provided to make the imputation more stable and feasible.

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Article

Randolph C. Rach

To provide a new proof of convergence of the Adomian decomposition series for solving nonlinear ordinary and partial differential equations based upon a thorough…

Abstract

Purpose

To provide a new proof of convergence of the Adomian decomposition series for solving nonlinear ordinary and partial differential equations based upon a thorough examination of the historical milieu preceding the Adomian decomposition method.

Design/methodology/approach

Develops a theoretical background of the Adomian decomposition method under the auspices of the Cauchy‐Kovalevskaya theorem of existence and uniqueness for solution of differential equations. Beginning from the concepts of a parametrized Taylor expansion series as previously introduced in the Murray‐Miller theorem based on analytic parameters, and the Banach‐space analog of the Taylor expansion series about a function instead of a constant as briefly discussed by Cherruault et al., the Adomian decompositions series and the series of Adomian polynomials are found to be a uniformly convergent series of analytic functions for the solution u and the nonlinear composite function f(u). To derive the unifying formula for the family of classes of Adomian polynomials, the author develops the novel notion of a sequence of parametrized partial sums as defined by truncation operators, acting upon infinite series, which induce these parametrized sums for simple discard rules and appropriate decomposition parameters. Thus, the defining algorithm of the Adomian polynomials is the difference of these consecutive parametrized partial sums.

Findings

The four classes of Adomian polynomials are shown to belong to a common family of decomposition series, which admit solution by recursion, and are derived from one unifying formula. The series of Adomian polynomials and hence the solution as computed as an Adomian decomposition series are shown to be uniformly convergent. Furthermore, the limiting value of the mth Adomian polynomial approaches zero as the index m approaches infinity for the prerequisites of the Cauchy‐Kovalevskaya theorem. The novel truncation operators as governed by discard rules are analogous to an ideal low‐pass filter, where the decomposition parameters represent the cut‐off frequency for rearranging a uniformly convergent series so as to induce the parametrized partial sums.

Originality/value

This paper unifies the notion of the family of Adomian polynomials for solving nonlinear differential equations. Further it presents the new notion of parametrized partial sums as a tool for rearranging a uniformly convergent series. It offers a deeper understanding of the elegant and powerful Adomian decomposition method for solving nonlinear ordinary and partial differential equations, which are of paramount importance in modeling natural phenomena and man‐made device performance parameters.

Details

Kybernetes, vol. 37 no. 7
Type: Research Article
ISSN: 0368-492X

Keywords

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