Stochastic theta methods for free stochastic differential equations
CoRR(2024)
摘要
We introduce free probability analogues of the stochastic theta methods for
free stochastic differential equations, which generalize the free
Euler-Maruyama method introduced by Schlüchtermann and Wibmer [27]. Under
some mild conditions, we prove the strong convergence and exponential stability
in mean square of the numerical solution. The free stochastic theta method with
θ=1 can inherit the exponential stability of original equations for any
given step size. Our method can offer better stability and efficiency than the
free Euler-Maruyama method. Moreover, numerical results are reported to confirm
these theoretical findings.
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