Expansion of Iterated Stratonovich Stochastic Integrals of Fifth, Sixth, Seventh and Eighth Multiplicities Based on Generalized Multiple Fourier Series

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The article is devoted to the construction of expansions of iterated Stratonovich stochastic integrals of fifth, sixth, seventh and eighth multiplicities based on the method of generalized multiple Fourier series converging in the sense of norm in the Hilbert space $L_2([t, T]^k),$ $k\in\mathbb{N}.$ Specifically, we mainly use multiple Fourier-Legendre series and multiple trigonometric Fourier series $(k=1,\ldots,8)$.

• The case of generalized multiple Fourier series in arbitrary complete orthonormal systems of functions in $L_2([t, T])$ is also considered for $k=1,\ldots,6$.
• Recently, expansions of iterated Stratonovich stochastic integrals of multiplicity $k,$ $k\in\mathbb{N}$ (the case of continuous weight functions and an arbitrary complete orthonormal system of functions in $L_2([t, T])$) have been obtained (Theorems 42, 44) but under one additional condition.
• The considered expansions converge in the mean-square sense and contain only one operation of the limit transition in contrast to its existing analogues.