A Milstein-type method for highly non-linear non-autonomous time-changed stochastic differential equations

08/27/2023

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A Milstein-type method is proposed for some highly non-linear non-autonomous time-changed stochastic differential equations (SDEs). The spatial variables in the coefficients of the time-changed SDEs satisfy the super-linear growth condition and the temporal variables obey some Hölder's continuity condition. The strong convergence in the finite time is studied and the convergence order is obtained.

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