[PDF] Top 20 An improved Milstein method for stiff stochastic differential equations

... classical Milstein method and no nonlinear algebra problems are encountered during ...IM method is, to a certain extent, improved even for the non-stiff prob- lem (see Table  in Section ), ... See full document

... EM method has its simple algebraic structure, cheap com- putational cost and acceptable convergence rate under the global Lipschitz condition, it has been attracting lots of attention ...EM method for SDEs ... See full document

... for stochastic differential equations (SDEs) has recently attracted an increasing ...been improved since the martingale techniques were introduced to in- vestigate the almost sure ... See full document

... rate equations, the Chemi- cal Langevin Equation (CLE) [15] is considered a very attractive choice in modeling many important biological ...of stochastic differ- ential equations, nonlinear and with ... See full document

... of stochastic systems, the stability analysis caused much more attention ...of stochastic differential equations themselves, it is difficult for us to get an- alytical solution of equations, ... See full document

... a stochastic differential equations, so investigation of conditions for existence of solution and obtain the analytical and numerical solutions of them are ...decomposition method for solution ... See full document

... of stochastic point equations which are a set of non-linear and strongly coupled stochastic differential ...proposed method considers an attenuation factor in the covariance matrix and ... See full document

... nonlinear stochastic differential equations (SDEs) without the global Lipschitz condition has become more and more ...(EM) method is convenient for computations and implementations, the ... See full document

... to stochastic differen- tial equations (SDEs) under the local Lipschitz ...(EM) method, the tamed Milstein method, the stopped EM, the backward EM, the backward forward EM, ...explicit ... See full document

... this method in approximating the solution of ...of stochastic Taylor expansions, up to ...and Milstein schemes had been proposed to apply them in practice or to study their ...Taylor method in ... See full document

... The authors hereby acknowledge the support of Covenant University Centre for Research, Innovation and Discovery (CUCRID). The authors appreciate the suggestions of the anonymous referees that has improved the ... See full document

... Apart from the stand-alone research interests of the strong convergence of numerical methods, the property of the strong convergence could also be used to improve the convergence rate of estimating the expectation of ... See full document

... In this section we describe a novel class of bridge constructs that require no tuning parameters, are simple to implement (even when only a subset of components are observed with Gaussian noise) and can account for ... See full document

... impulsive differential equations, please refer to Lakshmikantham et ...impulsive differential systems are very important and many results have been obtained in analysis of systems with impulse effect ... See full document

... of stochastic differential delay equations under the generalized Khasminskii-type conditions, Applied Mathematics and Computation, 217(2011), ...Euler method for impulsive stochastic ... See full document

... deterministic differential equations are fundamentals for the modeling in science, en- gineering and mathematical ...accurate differential equation models and solve more demanding ...be ... See full document

... differential equations, see Section . We dropped the measurements in the equations and model the uncertainty by random ...a stochastic collocation method of order , see Section ...costs, ... See full document

... In terms of the numeric procedure developed in this paper, within fi nance there are two applications that have potential for development. The fi rst application is to the forward rate equation formulated under the Musiela ... See full document

... [13]. Stiff differential equations also occur in other kind of studies, such as bio- chemistry, biomedical systems, weather prediction, mathematical biology and ...of stiff equations is ... See full document

... Itô stochastic systems. Based on LMI technique, stochastic Lyapunov function method is adopted to obtain a sufficient condition for the existence of a finite-time H ∞ ... See full document