جستجوی مقالات مرتبط با کلیدواژه « Stochastic differential equation » در نشریات گروه « ریاضی »

The main purpose of this paper is to introduce a new method to analyze the effects of the white and colored noise perturbations on the robotic arms. To show the efficiency of the presented idea the simplest manipulator, two link robotic arm, is considered. Most previous noise analyses of manipulators are done using mechanical or electrical modeling. Applying exact kinematic equations of the robots is the novelty of the proposed research. For this purpose, by adding white and colored noise terms in each angle function of the robotic arm, the end effector linear velocity is studied. Also, mechanical variation's effect on the final velocity in noisy space is considered. The longer the length of the links, the more the noise effect. Analysis of simulation results shows that the root mean square error in 2nd order is more than when angle functions are of the first order. Also, the mean square error is less when colored noise is added in comparison to the white noise. The Matlab programming is used to perform numerical examples to show the efficiency and accuracy of the presented idea.

In this paper, we develop a second-order optimality condition for optimal regular-singular control in the integral form of McKean-Vlasov stochastic differential equations. The coefficients of the dynamic depend on the state process as well as on its probability law. The control process has two components, the first being regular and absolutely continuous and the second is an increasing process (componentwise), continuous on the left with limits on the right with bounded variation. The regular control variable is allowed to enter into both drift and diffusion coefficients. The control domain is assumed to be convex. Our main result is proved by applying the L-derivatives with respect to probability law.

The main goal of this work is to develop and analyze an accurate trun-cated stochastic Runge–Kutta (TSRK2) method to obtain strong numeri-cal solutions of nonlinear one-dimensional stochastic differential equations (SDEs) with continuous Hölder diffusion coefficients. We will establish the strong L1-convergence theory to the TSRK2 method under the local Lipschitz condition plus the one-sided Lipschitz condition for the drift co-efficient and the continuous Hölder condition for the diffusion coefficient at a time T and over a finite time interval [0, T ], respectively. We show that the new method can achieve the optimal convergence order at a finite time T compared to the classical Euler–Maruyama method. Finally, nu-merical examples are given to support the theoretical results and illustrate the validity of the method.

Hilfer-Katugampola-type fractional stochastic differential equations with nonlocal conditions are considered in this paper. By using the fixed point theorem, the existence and uniqueness of solutions for the considered problem are proved. Ulam-Hyers stability for the considered problem is studied. Finally, an example is presented to show our main results.

In this paper, the Heston partial differential equation option pricing model is considered and the Legendre wavelet method (LWM) is used to solve this equation. The attributes of Legendre wavelets are used to reduce the PDEs problem into the solution of the ODEs system. The wavelet base is used in approximation due to its simplicity and efficiency. The method of creating Legendre wavelets and their main properties were briefly mentioned. Some numerical schemes have been compared with the LWM in the result.

In this paper‎, ‎we present a new approach to solving stochastic differential equations and the Vasicek equation by using Brownian wavelets and multiple Ito-integral‎. ‎Firstly‎, ‎the calculation of the multiple Ito-integral based on the structure of Brownian motion is presented and the error of Ito-integrate computation is minimized under this condition‎. ‎Then‎, ‎the Brownian wavelets 1D and 3D based on coefficients Brownian motion are introduced‎. ‎After that‎, ‎a system of linear and nonlinear equations of coefficients Brownian motion is obtained such that by solving this system the approximate solution of the Vasicek equation is obtained‎. In the last section, ‎some numerical examples are given.

In this paper, we use a Milstein scheme to develop a numerical technique for solving Stochastic differential equation which we had its deterministic form in our last article cite{Tepological}, we discuss the existence and uniqueness solution of deterministic and stochastic form, and then we show the advantages of the method with numerical example.

 We consider stochastic differential equation driven by αstable processes. Three methods of drifting split-step Euler, diffused split-step Euler and three-stage Milstein for approximation of solution are used. The strong convergence of these three methods is proven and the upper bounds of their stabilities are obtained and depicted.

‎The main focus of this paper is to examine the effects of Gaussian white noise and Gaussian colored noise perturbations on the voltage of RC and RLC electrical circuits‎. ‎For this purpose‎, ‎the input voltage is assumed to be corrupted by the white noise and the charge is observed at discrete time points‎. ‎The deterministic models will be transferred to stochastic differential equations and these models will be solved analytically using Ito's lemma‎. ‎Random colored noise excitations‎, ‎more close to real environmental excitations‎, ‎so Gaussian colored noise is considered in these electrical circuits‎. ‎Scince there is not always a closed form analytical solution for stochastic differential equations‎, ‎then these models will be solved numerically based on the Euler‎- ‎maruyama scheme‎. ‎The parameter estimation for these stochastic models is investigated using the least square estimator when the parameters are missing data that it is a concern in electrical engeineering‎. ‎Finally‎, ‎some numerical simulations via Matlab programming are carried out in order to show the efficiency and accuracy of the present work‎.

The population growth, is increase in the number of individuals in population and it depends on some random environment effects. There are several different mathematical models for population growth. These models are suitable tool to predict future population growth. One of these models is logistic model. In this paper, by using Feynman-Kac formula, the Adomian decomposition method is applied to compute the moments for the solution of logistic stochastic differential equation.

In the literature, the Euler-Maruyama (EM) method for approximation purposes of stochastic differential Equations (SDE) driven by α-stable Lévy motions is reported. Convergence in probability of that method was proven but it is surrounded by some ambiguities. To accomplish the but without ambiguities, this article has derived convergence in probability of numerical EM method based on diffusion given by semimartingales for SDEs driven by α-stable processes. Some examples are provided, their numerical solution are obtained and theoretical results are reconfirmed. The adopted method could be applied to other subclasses of semimartingales.

ýThe main purpose of this paper is to analyze the exchange rate volatility in Iran in the time period between 2011/11/27 and 2017/02/25 on a daily basis. As a tradable asset and as an important and effective economic variable, exchange rate plays a decisive role in the economy of a country. In a successful economic management, the modeling and prediction of the exchange rate volatility is essential for economic policies. Therefore, modeling and forecasting the changes in exchange rates for economic policies is vital. Foreign currency has the particular property of stochastic volatility, which can be modeled as a stochastic differential equation. In order to provide the best model, first, we studied the effectiveness of different stochastic models, drew upon the daily price of the exchange rate, and investigated the performance of these models. Finally, the best model was achieved by taking into account the numerical simulation and the mean square error, Akaikes (AIC), Schwarz’s Bayesian (SBIC), and the Hannan-Quinn (HQIC) ýcriteria.

In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation which can be solved by some numerical methods like Newton's or Broyden's methods. The capability of the simulation of Brownian motion with Schauder functions which are the integration of Haar functions enables us to find some reasonable approximate solutions. Two test examples and the application of the presented method for the general stock model are considered to demonstrate the efficiency, high accuracy and the simplicity of the presented method.

It is known that a stochastic differential equation (SDE) induces two probabilistic objects, namely a difusion process and a stochastic flow. While the diffusion process is determined by the in nitesimal mean and variance given by the coefficients of the SDE, this is not the case for the stochastic flow induced by the SDE. In order to characterize the stochastic flow uniquely the in nitesimal covariance given by the coefficients of the SDE is needed in addition. The SDEs we consider here are obtained by a weak perturbation of a rigid rotation by random elds which are white in time. In order to obtain information about the stochastic flow induced by this kind of multiscale SDEs we use averaging for the in nitesimal covariance. The main result here is an explicit determination of the coefficients of the averaged SDE for the case that the diffusion coefficients of the initial SDE are polynomial. To do this we develop a complex version of Cholesky decomposition algorithm.

In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differential equations system from this equation, it could be approximated or solved numerically by different numerical methods. In the case of linear stochastic differential equations system by Computing fundamental matrix of this system, it could be calculated based on the exact solution of this system. Finally, this stochastic equation is solved by numerically method like Euler-Maruyama and Milstein. Also its Asymptotic stability and statistical concepts like expectation and variance of solutions are discussed.

The edge detour index polynomials were recently introduced for computing the edge detour indices. In this paper we find relations among edge detour polynomials for the 2-dimensional graph of $TUC_4C_8(S)$ in a Euclidean plane and $TUC4C8(S)$ nanotorus.

In this paper, we present an application of the stochastic calculus to the problem of modeling electrical networks. The filtering problem have an important role in the theory of stochastic differential equations(SDEs). In this article, we present an application of the continuous Kalman-Bucy filter for a RL circuit. The deterministic model of the circuit is replaced by a stochastic model by adding a noise term in the source. The analytic solution of the resulting stochastic integral equations are found using the Ito formula.

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

Stochastic differential equations(SDEs), arise from physical systems that possess inherent noise and certainty. We derive a SDE for electrical circuits. In this paper, we will explore the close relationship between the SDE and autoregressive(AR) model. We will solve SDE related to RC circuit with using of AR(1) model (Markov process) and however with Euler-Maruyama(EM) method. Then, we will compare this solutions. Numerical simulations in MATLAB are obtained.