Analysis of asymptotic mean-square stability of a class of Runge–Kutta schemes for linear systems of stochastic differential equations

Haghighi, Amir; Hosseini, Seyed Mohammad

doi:10.1016/j.matcom.2014.05.002

Cited by 10 publications

(5 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark When

{\overset{k}{true}}_{1} = {\overset{k}{true}}_{1} = 0

in Assumption 2.2, the asymptotic mean‐square boundedness of solution for the system () will degenerate into asymptotic mean‐square stability. Similar definition can be found in the literature 43,44 …”

Section: Asymptotic Mean‐square Boundednessmentioning

confidence: 77%

Asymptotic mean‐square boundedness of the numerical solutions for stochastic complex‐valued neural networks with jumps

Yang²,

Wang

et al. 2022

Math Methods in App Sciences

View full text Add to dashboard Cite

The paper devoted to asymptotic mean-square boundedness of several numerical methods for stochastic complex-valued neural networks with Poisson jumps.The definition of asymptotic mean-square boundedness of the numerical solution is presented, and some sufficient conditions for the underlying systems which are asymptotic mean-square boundedness are derived. By taking the advantage of the compensated split-step backward Euler (CSSBE) method and compensated backward Euler (CBE) method, sufficient criteria promising the asymptotic mean-square boundedness of CVNNs without any restriction on time stepsize, while the split-step backward Euler (SSBE) method and backward Euler (BE) method can derive asymptotic mean-square boundedness under a time stepsize constraint. The obtained theoretical results show that the compensated numerical methods own an incredible advantage over the noncompensated numerical methods on the part of asymptotic mean-square boundedness. Finally, an example is proposed and analyzed to demonstrate the effectiveness and feasibility of the proposed results.

show abstract

“…Remark When

{\overset{k}{true}}_{1} = {\overset{k}{true}}_{1} = 0

Section: Asymptotic Mean‐square Boundednessmentioning

confidence: 77%

Asymptotic mean‐square boundedness of the numerical solutions for stochastic complex‐valued neural networks with jumps

Yang²,

Wang

et al. 2022

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…By the given condition (11), for any > 0, there exists > 0, such that when ‖ ‖ < , ‖ ( , )‖ ≤ ‖ ‖, = 0, 1, . .…”

Section: Theoremmentioning

confidence: 99%

“…Remark 15. Obviously, (11) and (46) do not imply each other, which motivates us to search for other less conservative conditions in the future.…”

Section: Globally Asymptotic Stabilizationmentioning

confidence: 99%

“…A series of works on robustly exponential stability can be found in [3][4][5][6]. While the th moment stability were discussed in [7,8], in particular, the asymptotic mean square stability has been studied for a long time; see [9][10][11][12][13]. The stabilizability of linear stochastic control systems has been investigated by [9,10,[12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…The state responses of the unforced system ( = 0).Obviously, 0 ( , ) and 1 ( , ) satisfy condition(11). According to Theorem 2, a feasible solution is derived by solving LMI(12): control gain matrix is = −1 = [−1.1831 −1.5993] .…”

mentioning

confidence: 99%

See 2 more Smart Citations

Feedback Stabilization for a Class of Nonlinear Stochastic Systems with State‐ and Control‐Dependent Noise

Wang

Zhang

2014

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

High strong order stochastic Runge-Kutta methods for Stratonovich stochastic differential equations with scalar noise

Xiao

Tang

2015

Numer Algor

View full text Add to dashboard Cite

Analysis of asymptotic mean-square stability of a class of Runge–Kutta schemes for linear systems of stochastic differential equations

Cited by 10 publications

References 13 publications

Asymptotic mean‐square boundedness of the numerical solutions for stochastic complex‐valued neural networks with jumps

Asymptotic mean‐square boundedness of the numerical solutions for stochastic complex‐valued neural networks with jumps

Feedback Stabilization for a Class of Nonlinear Stochastic Systems with State‐ and Control‐Dependent Noise

High strong order stochastic Runge-Kutta methods for Stratonovich stochastic differential equations with scalar noise

Contact Info

Product

Resources

About