Mean-square stability of Milstein method for linear hybrid stochastic delay integro-differential equations

Rathinasamy, A.; Balachandran, K.

doi:10.1016/j.nahs.2008.09.015

Cited by 25 publications

(15 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the following tests, we show the influence of stepsize h on mean-square stability of the SSBE method and compare our results with that obtained in [1,[3][4]. The data used in all figures are obtained by the mean square of data by 100 trajectories, that is, Ω :…”

Section: Numerical Experimentsmentioning

confidence: 98%

“…This test equation has been investigated in [3]. It is easily verified that conditions (2) is satisfied.…”

Section: Numerical Experimentsmentioning

confidence: 98%

“…Our objective is to illustrate intuitively the stability obtained in the previous section. Furthermore, we compare the restrictions on stepsize of the stable SSBE method with that of the Euler method and Milstein method (see [1,[3][4]). …”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Figure 1 illustrates the MSstability of numerical solution obtained by the SSBE method when h = 0.5. However, applied to the same test equation, the Milstein method is unstable when the stepsize h = 0.5 [3] and is MS-stable when the stepsize 0 < h < 1/9. This shows that in this sense the SSBE method is superior to the Milstein method.…”

Section: Numerical Experimentsmentioning

confidence: 99%

See 3 more Smart Citations

A note on stability of the split-step backward Euler method for linear stochastic delay integro-differential equations

2012

View full text Add to dashboard Cite

In the literature (Tan and Wang, 2010), Tan and Wang investigated the convergence of the split-step backward Euler (SSBE) method for linear stochastic delay integro-differential equations (SDIDEs) and proved the mean-square stability of SSBE method under some condition. Unfortunately, the main result of stability derived by the condition is somewhat restrictive to be applied for practical application. This paper improves the corresponding results. The authors not only prove the mean-square stability of the numerical method but also prove the general mean-square stability of the numerical method. Furthermore, an example is given to illustrate the theory.

show abstract

Section: Numerical Experimentsmentioning

confidence: 98%

“…This test equation has been investigated in [3]. It is easily verified that conditions (2) is satisfied.…”

Section: Numerical Experimentsmentioning

confidence: 98%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

See 2 more Smart Citations

A note on stability of the split-step backward Euler method for linear stochastic delay integro-differential equations

2012

View full text Add to dashboard Cite

show abstract

“…For example, [25] discusses the mean square stability of SDDEs with constant coefficients and [22] obtains also mean-square stability for SDDEs with integral part. Based on these papers, to the best of our knowledge, the alsmost sure exponential stability of Milstein method for SDDEs with jump has never been considered so far.…”

Section: Introductionmentioning

confidence: 99%

A Note on the Almost Sure Exponential Stability of the Milstein Method for Stochastic Delay Differential Equations With Jumps

Rouz¹,

Ahmadian²,

Akbarfam³

et al. 2017

Int. J. of Pure and Appl. Math.

View full text Add to dashboard Cite

In this paper we consider the Milstein method to investigate the almost sure exponential stability for nonlinear stochastic delay differential equations (SDDEs) with jump diffusion, that is, processes that change only by jumps. The class of jump-diffusion SDDEs that admits explicit solutions is rather limited. In this regard, we employ the continuous and discrete semimartingale convergence theorem. It is shown that the Milstein method reproduces the almost sure exponential stability under an additional linear growth condition on drift and the function L 1 g. In the numerical section we present the results by simulating the method on kind of equations.

show abstract

Some Results on Almost Sure Stability of Non-Autonomous Stochastic Differential Equations with Markovian Switching

Dieu

2016

Vietnam J. Math.

View full text Add to dashboard Cite

Mean-square stability of Milstein method for linear hybrid stochastic delay integro-differential equations

Cited by 25 publications

References 15 publications

A note on stability of the split-step backward Euler method for linear stochastic delay integro-differential equations

A note on stability of the split-step backward Euler method for linear stochastic delay integro-differential equations

A Note on the Almost Sure Exponential Stability of the Milstein Method for Stochastic Delay Differential Equations With Jumps

Some Results on Almost Sure Stability of Non-Autonomous Stochastic Differential Equations with Markovian Switching

Contact Info

Product

Resources

About