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The article is devoted to optimization of the mean-square approximationprocedures for iterated Ito stochastic integrals of multiplicities 1 to 5. Thementioned stochastic integrals are part of strong numerical methods withconvergence orders 1.0, 1.5, 2.0, and 2.5 for Ito stochastic differentialequations with multidimensional non-commutative noise based on the unifiedTaylor-Ito expansion and multiple Fourier-Legendre series converging in thesense of norm in Hilbert space $L_2([t, T]^k)$ $(k=1,\ldots,5).$ In thisarticle we use multiple Fourier-Legendre series within the framework of themethod of expansion and mean-square approximation of iterated Ito stochasticintegrals based on generalized multiple Fourier series. We show that thelengths of sequences of independent standard Gaussian random variables requiredfor the mean-square approximation of iterated Ito stochastic integrals ofmultiplicities 1 to 5 can be significantly reduced without the loss of themean-square accuracy of approximation for these stochastic integrals.

journal of physics. conference series

Optimization of the Mean-Square Approximation Procedures for Iterated  Ito Stochastic Integrals of Multiplicities 1 to 5 from the Unified Taylor-Ito  Expansion Based on Multiple Fourier-Legendre Series