Mean-Square Approximation of Iterated Ito and Stratonovich Stochastic Integrals of Multiplicities 1 to 6 from the Taylor-Ito and Taylor-Stratonovich Expansions Using Legendre Polynomials

Understand

The article is devoted to the practical material on expansions and mean-square approximations of specific iterated Ito and Stratonovich stochastic integrals of multiplicities 1 to 6 with respect to components of the multidimensional Wiener process on the base of the method of generalized multiple Fourier series.

• More precisely, we used the multiple Fourier--Legendre series converging in the sense of norm in the space $L_2([t, T]^k)$ $(k=1,\ldots,6)$ for approximation of iterated Ito and Stratonovich stochastic integrals.
• The considered iterated Ito and Stratonovich stochastic integrals are part of the stochastic Taylor expansions (Taylor-Ito and Taylor-Stratonovich expansions).
• Therefore, the results of the article can be useful for construction of the high-order strong numerical methods for Ito stochastic differential equations.