Asymptotic mean-square stability of two-step Maruyama schemes for stochastic differential equations
نویسندگان
چکیده
منابع مشابه
On exponential mean-square stability of two-step Maruyama methods for stochastic delay differential equations
We are concerned with the exponential mean-square stability of two-step Maruyama methods for stochastic differential equations with time delay. We propose a family of schemes and prove that it can maintain the exponential mean-square stability of the linear stochastic delay differential equation for every step size of integral fraction of the delay in the equation. Numerical results for linear ...
متن کاملMulti - step Maruyama methods for stochastic delay differential equations ∗
In this paper the numerical approximation of solutions of Itô stochastic delay differential equations is considered. We construct stochastic linear multi-step Maruyama methods and develop the fundamental numerical analysis concerning their Lp-consistency, numerical Lp-stability and Lpconvergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-squa...
متن کاملMean-square and Asymptotic Stability of Numerical Methods for Stochastic Ordinary Diierential Equations
Stability analysis of numerical methods for ordinary diierential equations is motivated by the question \for what choices of stepsize does the numerical method reproduce the characteristics of the test equation?" We study a linear test equation with a multiplicative noise term, and consider mean-square and asymptotic stability of a stochastic version of the Theta Method. We extend some mean-squ...
متن کاملA structural analysis of asymptotic mean-square stability for multi-dimensional linear stochastic differential systems
We are concerned with a linear mean-square stability analysis of numerical methods applied to systems of stochastic differential equations (SDEs) and, in particular, consider the θ-Maruyama and the θ-Milstein method in this context. We propose a technique, based on the vectorisation of matrices and the Kronecker product, to deal with the matrix expressions arising in this analysis and provide t...
متن کاملMean-Square and Asymptotic Stability of the Stochastic Theta Method
Stability analysis of numerical methods for ordinary differential equations (ODEs) is motivated by the question “for what choices of stepsize does the numerical method reproduce the characteristics of the test equation?” We study a linear test equation with a multiplicative noise term, and consider mean-square and asymptotic stability of a stochastic version of the theta method. We extend some ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2014
ISSN: 0377-0427
DOI: 10.1016/j.cam.2013.10.002