Well posedness of second-order impulsive fractional neutral stochastic differential equations

<abstract><p>In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step $ (\alpha, \beta) $-Milstein scheme strongly convergence to the exact solution with order $ 1.0 $ in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters $ \alpha, \beta $. Finally, numerical examples illustrate the effectiveness of the theoretical results.</p></abstract>

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Simulating systems of Itô SDEs with split-step $ (\alpha, \beta) $-Milstein scheme

Ranjbar

Torkzadeh

Băleanu

et al. 2023

MATH

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Well posedness of second-order impulsive fractional neutral stochastic differential equations

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References 15 publications

Simulating systems of Itô SDEs with split-step $ (\alpha, \beta) $-Milstein scheme

Simulating systems of Itô SDEs with split-step $ (\alpha, \beta) $-Milstein scheme

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