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On exponential mean-square stability of two-step Maruyama methods for stochastic delay differential equations

Wanrong Cao, Zhongqiang Zhang
2013 Journal of Computational and Applied Mathematics  
We are concerned with the exponential mean-square stability of two-step Maruyama methods for stochastic differential equations with time delay.  ...  Numerical results for linear and nonlinear equations show that this family of two-step Maruyama methods exhibits better stability than previous two-step Maruyama methods.  ...  Taketomo Mitsui for their helpful suggestions for improving the paper.  ... 
doi:10.1016/j.cam.2012.12.026 fatcat:6jipsev7ojbphnuu7sudbr4roa

Consistency Techniques for Hybrid Simulations

Marco Bottalico, Marc Herbstritt
2011 International Conference on Logic Programming  
The goal of this paper is to show consistency techniques methods and hybrid stochastic/deterministic models to describe biochemical systems and their behaviour through the ordinary differential equations  ...  On the one hand, it is necessary to describe some parts in a rigorous and accurate numerical method (for example methods based on ordinary differential equations or stochastic methods).  ...  This method include one-step methods and multi-step methods; in general these methods do not guarantee the existence of a solution within a given bound.  ... 
doi:10.4230/lipics.iclp.2011.255 dblp:conf/iclp/Bottalico11 fatcat:zmn56647o5ajvfzlndriqo3krq

Page 8113 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
Petersburg) Three-step strong numerical methods of 1.0 and 1.5 orders of accuracy for stochastic differential It6 equations. (Russian. English, Russian and Ukrainian summaries) Problemy Upravlen.  ...  Stochastic differential equations in It6 integral form are consid- ered. Three step strong numerical methods of the order 1.0 and 1.5 are developed. The proposed methods are of Runge-Kutta type.  ... 

Page 7969 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
The paper under review presents a variable step size method for the time discretization of stochastic differential equations, when one seeks a pathwise convergent approximation.  ...  characterization of Markov solutions for stochastic differential equations with jumps.  ... 

The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method

Yousef Alnafisah
2018 Abstract and Applied Analysis  
In this paper we describe how the Fourier series expansion of Wiener process can be used to simulate a two-dimensional stochastic differential equation (SDE) using Matlab program.  ...  Our numerical experiments use Matlab to show how our truncation of Itô'-Taylor expansion at an appropriate point produces Milstein method for the SDE.  ...  Numerical Method for Approximating the SDEs There are many numerical methods for solving stochastic differential equation; here we will mention two important schemes.  ... 
doi:10.1155/2018/3805042 fatcat:a44pfz2lqzaenkblj3b6i6nbae

Effective Computation of Stochastic Protein Kinetic Equation by Reducing Stiffness via Variable Transformation [article]

Lijin Wang
2014 arXiv   pre-print
The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated  ...  For such situation, we provide a method of reducing stiffness of the stochastic protein kinetic equation by means of a kind of variable transformation.  ...  One of the most well-known numerical methods for solving stochastic differential equations (SDEs) is the Euler-Maruyama method, which is, however, only consistent to SDEs of Itô type.  ... 
arXiv:1411.3452v1 fatcat:u5abcr446fhynpkf7x65pbohxa

Qualitative Analysis on Differential, Fractional Differential, and Dynamic Equations and Related Topics

Said R. Grace, Taher S. Hassan, Shurong Sun, Elvan Akin
2016 Discrete Dynamics in Nature and Society  
Yuan et al. introduced and analyzed split-step theta (SST) method for nonlinear neutral stochastic differential delay equations (NSDDEs).  ...  The asymptotic mean square stability of the split-step theta (SST) method is considered for nonlinear neutral stochastic differential equations.  ...  Yuan et al. introduced and analyzed split-step theta (SST) method for nonlinear neutral stochastic differential delay equations (NSDDEs).  ... 
doi:10.1155/2016/3590319 fatcat:7s6zim5v7bdgpoiomgn6sje2gq

High-order strong methods for stochastic differential equations with colored noises

Shuanglin Sun, Yun-An Yan
2019 Chemical Physics Letters  
The key difficulty to develop efficient high-order methods for integrating stochastic differential equations lies in the calculations of the multiple stochastic integrals.  ...  Based on the calculated stochastic integrals, we obtain simple fourth-order and third-order strong methods for equations with a single and multiple noises, respectively.  ...  Furthermore, although the method is derived for autonomous linear stochastic differential equations, it can be readily extended to general equations as well. FIG. 1 . 1 FIG.1.  ... 
doi:10.1016/j.cplett.2019.136766 fatcat:7rep3pagqba5bkq334gmf4kkzy

Page 8024 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
In Chapter 5, strong discrete-time higher-order one-step and two-step approximations are systematically proposed and studied.  ...  In Chapter 4, the four step scheme, devised by the same authors, is presented. This method allows one to solve, under appropriate conditions, equation (1) in any time interval.  ... 

Stability of weak numerical schemes for stochastic differential equations

N. Hofmann, E. Platen
1994 Computers and Mathematics with Applications  
A relatively strong notion of stability for a special type of test equations is proposed. These are stochastic differential equations with multiplicative noise.  ...  This paper considers numerical stability and convergence of weak schemes solving stochastic differential equations.  ...  A deterministic one-step method (2) is called asymptotically numerically stable for a given differential equation if there exist positive constants As and M such that (5) for any two solutions Y, Y of  ... 
doi:10.1016/0898-1221(94)00185-5 fatcat:3f3xicpstvgepievwezbhcxcbe

Stability of weak numerical schemes for stochastic differential equations

Norbert Hofmann
1995 Mathematics and Computers in Simulation  
A relatively strong notion of stability for a special type of test equations is proposed. These are stochastic differential equations with multiplicative noise.  ...  This paper considers numerical stability and convergence of weak schemes solving stochastic differential equations.  ...  A deterministic one-step method (2) is called asymptotically numerically stable for a given differential equation if there exist positive constants As and M such that (5) for any two solutions Y, Y of  ... 
doi:10.1016/0378-4754(93)e0067-f fatcat:txcd2xd7arhlzdr5uezjbp7fmu

Adaptive time-stepping for the strong numerical solution of stochastic differential equations

Silvana Ilie, Kenneth R. Jackson, Wayne H. Enright
2014 Numerical Algorithms  
Models based on stochastic differential equations are of high interest today due to their many important practical applications.  ...  This paper focuses on the strong numerical solution of stochastic differential equations in Itô form, driven by multiple Wiener processes.  ...  According to Gaines & Lyons [11] , a numerical method of strong order 1 is required for an adaptive time-stepping method to converge to the strong solution of a stochastic differential equation.  ... 
doi:10.1007/s11075-014-9872-6 fatcat:j23xgsxrnvdhdpuri2ptqoftza

On One-Step Method of Euler-Maruyama Type for Solution of Stochastic Differential Equations Using Varying Stepsizes

Sunday Jacob Kayode, Akeem Adebayo Ganiyu, Adegoke Sule Ajiboye
2016 OALib  
In this work, a one-step method of Euler-Maruyama (EMM) type has been developed for the solution of general first order stochastic differential equations (SDEs) using Itô integral equation as basis tool  ...  The effect of varying stepsizes on the numerical solution is also examined for the SDEs. Two problems of first order SDEs are solved.  ...  Under this section, Itô integral form of stochastic differential Equation (3) stated in Equation (4) is used as the basis for the derivation of one-step Euler-Maruyama method.  ... 
doi:10.4236/oalib.1102247 fatcat:vztfdv3tmfgizgxwftjjw4rifq

Runge-Kutta Algorithm for the Numerical Integration of Stochastic Differential Equations

N. Jeremy Kasdin
1995 Journal of Guidance Control and Dynamics  
Fig.4 Two-link robot example. Example 3. Lastly, the RK integrator of method B was applied to a nonlinear set of stochastic differential equations.  ...  Thus, single-step, fixed-step-size methods are the best approach for simulating stochastic differential equations. Again, the most common integrators of this class are RK algorithms.  ... 
doi:10.2514/3.56665 fatcat:6rewyfgywrflfj5xgzymtxiqkm

Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions

Howard Salis, Yiannis Kaznessis
2005 Journal of Chemical Physics  
In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations.  ...  In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs  ...  ACKNOWLEDGMENTS We thank Chetan Gadgil for discussion of the manuscript and the Supercomputing Institute of Minnesota for computational resources. This work is supported by an NIH training grant ͑No.  ... 
doi:10.1063/1.1835951 pmid:15740306 fatcat:w3hshfo5tbgqdnrj6p6mkpxjmm
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