Efficient numerical integrators for stochastic models
نویسندگان
چکیده
منابع مشابه
Efficient numerical integrators for stochastic models
The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for general SDEs can be derived using the Trotter expansion. It follows that, in the stochastic case, some care is required in splitting the stochastic generator. We t...
متن کاملEfficient Strong Integrators for Linear Stochastic Systems
We present numerical schemes for the strong solution of linear stochastic differential equations driven by an arbitrary number of Wiener processes. These schemes are based on the Neumann (stochastic Taylor) and Magnus expansions. Firstly, we consider the case when the governing linear diffusion vector fields commute with each other, but not with the linear drift vector field. We prove that nume...
متن کاملEfficient Numerical Algorithms for Balanced Stochastic Truncation
We propose an efficient numerical algorithm for relative error model reduction based on balanced stochastic truncation. The method uses full-rank factors of the Gramians to be balanced versus each other and exploits the fact that for large-scale systems these Gramians are often of low numerical rank. We use the easy-to-parallelize sign function method as the major computational tool in determin...
متن کاملBackward Error Analysis for Numerical Integrators Backward Error Analysis for Numerical Integrators
We consider backward error analysis of numerical approximations to ordinary diie-rential equations, i.e., the numerical solution is formally interpreted as the exact solution of a modiied diierential equation. A simple recursive deenition of the modiied equation is stated. This recursion is used to give a new proof of the exponentially closeness of the numerical solutions and the solutions to a...
متن کاملStochastic Lie Group Integrators
We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold. Given a Lie group action that generates transport along the manifold, we pull back the stochastic flow on the manifold to the Lie group via the action, and subsequently pull back the flow to the corresponding Lie alge...
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: Physica A: Statistical Mechanics and its Applications
سال: 2006
ISSN: 0378-4371
DOI: 10.1016/j.physa.2005.06.090